Theorem 19.42 1096

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 1095	. 2 |- (E.x(ps /\ ph) <-> (E.xps /\ ph))
3		exancom 1054	. 2 |- (E.x(ph /\ ps) <-> E.x(ps /\ ph))
4		ancom 435	. 2 |- ((ph /\ E.xps) <-> (E.xps /\ ph))
5	2, 3, 4	3bitr4 183	1 |- (E.x(ph /\ ps) <-> (ph /\ E.xps))

Syntax hints:   -> wi 3   <-> wb 146   /\ wa 223  A.wal 954  E.wex 980

This theorem is referenced by:  19.42v 1308  cbvex2 1317  euan 1428

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-4 973  ax-5o 975  ax-6o 978

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 981

Copyright terms: Public domain