Theorem 19.29r 1072

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 1071	. 2 |- ((A.xps /\ E.xph) -> E.x(ps /\ ph))
2		ancom 435	. 2 |- ((E.xph /\ A.xps) <-> (A.xps /\ E.xph))
3		exancom 1054	. 2 |- (E.x(ph /\ ps) <-> E.x(ps /\ ph))
4	1, 2, 3	3imtr4 219	1 |- ((E.xph /\ A.xps) -> E.x(ph /\ ps))

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

This theorem is referenced by:  19.29r2 1073  19.29x 1074  eu2 1396  imadif 3574  kmlem6 4770  faimpex 10438

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

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

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