Theorem 19.29r 1423

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 1421	. 2 |- ((A.xps /\ E.xph) -> E.x(ps /\ ph))
2		ancom 482	. 2 |- ((E.xph /\ A.xps) <-> (A.xps /\ E.xph))
3		exancom 1401	. 2 |- (E.x(ph /\ ps) <-> E.x(ps /\ ph))
4	1, 2, 3	3imtr4i 236	1 |- ((E.xph /\ A.xps) -> E.x(ph /\ ps))

Syntax hints:   -> wi 3   /\ wa 240  A.wal 1296  E.wex 1326

This theorem is referenced by:  19.29r2 1424  19.29x 1425  exan 1463  equvini 1531  eu2 1791  imadif 4493  kmlem6 5932  bnj1027 12882  bnj1028 12883  bnj849 13318

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1305  ax-4 1319  ax-5o 1321

This theorem depends on definitions:  df-bi 164  df-an 242  df-ex 1327

Copyright terms: Public domain