Theorem 19.42 775

Description: Theorem 19.42 of [Margaris] p. 90.

Hypothesis

Ref	Expression
19.42.1	|- (ph -> A.xph)

Assertion

Ref	Expression
19.42	|- (E.x(ph /\ ps) <-> (ph /\ E.xps))

Proof of Theorem 19.42

Step	Hyp	Ref	Expression
1		19.42.1	. . 3 |- (ph -> A.xph)
2	1	19.41 774	. 2 |- (E.x(ps /\ ph) <-> (E.xps /\ ph))
3		exancom 736	. 2 |- (E.x(ph /\ ps) <-> E.x(ps /\ ph))
4		ancom 333	. 2 |- ((ph /\ E.xps) <-> (E.xps /\ ph))
5	2, 3, 4	3bitr4 158	1 |- (E.x(ph /\ ps) <-> (ph /\ E.xps))

Syntax hints:   -> wi 2   <-> wb 127   /\ wa 196  A.wal 672  E.wex 678

This theorem is referenced by:  19.42v 966  cbvex2 975

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-gen 677

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679

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