Theorem 5.8 (y \in x \in \omega \c y \i x)
Note 1 (A \ident \setof x \Each y\in x(y\i x))
By S
Note 2 (t \in A \Iff \Each y \in t (y \i t) \And t \in \U)
By 08.3;.1
Checked with rules.tex : 84 level: 2
Note 3 (\e \in A)
By .2;09.19,09.12
Checked with rules.tex : 148 level: 2
Note 4 (x \in A )
By G
Note 5 (x \in \U)
By 09.20;.4
Checked with rules.tex : 84 level: 0
Note 6 \Each y \in x(y \i x)
By .2;.4
Checked with rules.tex : 116 level: 2
Note 7
Line 1 (y \in \scsr x \c y \in x \Or y = x
By 4.7
Checked with rules.tex : 44 level: 0
Line 2 \c y \i x \Or y = x
By .6
Checked with rules.tex : 709 level: 0
Line 3 \c y \i x
By 011.14
Checked with rules.tex : 663 level: 0
Line 4 \c y \i \scsr x )
By 011.10;( 4.5;(09.20;.4))
Checked with rules.tex : 3033 level: 2
Note 8 (\scsr x \in A)
By .2;(4.3;.5),(.7 U)
Checked with rules.tex : 3266 level: 2
Note 9 (x \in A \c \scsr x \in A)
By .8 H .4
Checked with rules.tex : 2098 level: 0
Note 10 (\omega \i A)
By 5.7;.3,(.9 U)
Checked with rules.tex : 3124 level: 2
Note 11
Line 1 (y \in x \And x \in \omega\c y \in x \And x \in A
By 011.7;.10
Checked with rules.tex : 969 level: 2
Line 2 \c y \in x \And \Each y \in x(y \i x)
By .2
Checked with rules.tex : 428 level: 2
Line 3 \c y \i x)
By
Checked with rules.tex : 2446 level: 2
QED By .11
Checked with rules.tex : 44 level: 2
Proof checked.