Theorem 19.25 1721

Description: Theorem 19.25 of [Margaris] p. 90.

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 1712	. . . 4 |- (E.x(ph -> ps) <-> (A.xph -> E.xps))
2	1	biimpi 224	. . 3 |- (E.x(ph -> ps) -> (A.xph -> E.xps))
3	2	alimi 1627	. 2 |- (A.yE.x(ph -> ps) -> A.y(A.xph -> E.xps))
4		exim 1675	. 2 |- (A.y(A.xph -> E.xps) -> (E.yA.xph -> E.yE.xps))
5	3, 4	syl 13	1 |- (A.yE.x(ph -> ps) -> (E.yA.xph -> E.yE.xps))

Syntax hints:   -> wi 3  A.wal 1584  E.wex 1615

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1593  ax-4 1608  ax-5o 1610

This theorem depends on definitions:  df-bi 220  df-an 339  df-ex 1616

Copyright terms: Public domain