Theorem 19.29 1421

Description: Theorem 19.29 of [Margaris] p. 90. (The proof was shortened by Andrew Salmon, 13-May-2011.)

Assertion

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

Proof of Theorem 19.29

Step	Hyp	Ref	Expression
1		pm3.2 305	. . . 4 |- (ph -> (ps -> (ph /\ ps)))
2	1	alimi 1338	. . 3 |- (A.xph -> A.x(ps -> (ph /\ ps)))
3		exim 1386	. . 3 |- (A.x(ps -> (ph /\ ps)) -> (E.xps -> E.x(ph /\ ps)))
4	2, 3	syl 12	. 2 |- (A.xph -> (E.xps -> E.x(ph /\ ps)))
5	4	imp 377	1 |- ((A.xph /\ E.xps) -> E.x(ph /\ ps))

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

This theorem is referenced by:  19.29r 1423  19.29x 1425  exanOLD 1464  equvini 1531  r19.29OLD 2228

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