Theorem 19.29r 753

Description: Variation of Theorem 19.29 of [Margaris] p. 90.

Assertion

Ref	Expression
19.29r	|- ((E.xph /\ A.xps) -> E.x(ph /\ ps))

Proof of Theorem 19.29r

Step	Hyp	Ref	Expression
1		19.29 752	. 2 |- ((A.xps /\ E.xph) -> E.x(ps /\ ph))
2		ancom 333	. 2 |- ((E.xph /\ A.xps) <-> (A.xps /\ E.xph))
3		exancom 736	. 2 |- (E.x(ph /\ ps) <-> E.x(ps /\ ph))
4	1, 2, 3	3imtr4 192	1 |- ((E.xph /\ A.xps) -> E.x(ph /\ ps))

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

This theorem is referenced by:  eu2 1023  imadif 2714  kmlem6 3585

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-gen 677

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

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