Theorem 19.25 1603

Description: Theorem 19.25 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
19.25	|- (A.yE.x(ph -> ps) -> (E.yA.xph -> E.yE.xps))

Proof of Theorem 19.25

Step	Hyp	Ref	Expression
1		19.35 1600	. . . 4 |- (E.x(ph -> ps) <-> (A.xph -> E.xps))
2	1	biimpi 186	. . 3 |- (E.x(ph -> ps) -> (A.xph -> E.xps))
3	2	alimi 1559	. 2 |- (A.yE.x(ph -> ps) -> A.y(A.xph -> E.xps))
4		exim 1575	. 2 |- (A.y(A.xph -> E.xps) -> (E.yA.xph -> E.yE.xps))
5	3, 4	syl 15	1 |- (A.yE.x(ph -> ps) -> (E.yA.xph -> E.yE.xps))

This proof depends on syntax axioms:   -> wi 4  A.wal 1540  E.wex 1541

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557

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

This theorem is used by: (None)