Theorem 19.29 1596

Description: Theorem 19.29 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.) (Proof 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		pm3.2 434	. . . 4 |- (ph -> (ps -> (ph /\ ps)))
2	1	alimi 1559	. . 3 |- (A.xph -> A.x(ps -> (ph /\ ps)))
3		exim 1575	. . 3 |- (A.x(ps -> (ph /\ ps)) -> (E.xps -> E.x(ph /\ ps)))
4	2, 3	syl 15	. 2 |- (A.xph -> (E.xps -> E.x(ph /\ ps)))
5	4	imp 418	1 |- ((A.xph /\ E.xps) -> E.x(ph /\ ps))

Syntax hints:   -> wi 4   /\ wa 358  A.wal 1540  E.wex 1541

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557

This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542

This theorem is referenced by:  19.29r  1597  19.29x  1599  equs4  1959  equvini  1987  fnfrec  6321