Theorem 19.24 762

Description: Theorem 19.24 of [Margaris] p. 90.

Assertion

Ref	Expression
19.24	|- ((A.xph -> A.xps) -> E.x(ph -> ps))

Proof of Theorem 19.24

Step	Hyp	Ref	Expression
1		19.2 713	. . 3 |- (A.xps -> E.xps)
2	1	syl3 18	. 2 |- ((A.xph -> A.xps) -> (A.xph -> E.xps))
3		19.35 754	. 2 |- (E.x(ph -> ps) <-> (A.xph -> E.xps))
4	2, 3	sylibr 175	1 |- ((A.xph -> A.xps) -> E.x(ph -> ps))

Syntax hints:   -> wi 2  A.wal 672  E.wex 678

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-gen 677

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679

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