Theorem 19.24 1083

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 1030	. . 3 |- (A.xps -> E.xps)
2	1	imim2i 17	. 2 |- ((A.xph -> A.xps) -> (A.xph -> E.xps))
3		19.35 1075	. 2 |- (E.x(ph -> ps) <-> (A.xph -> E.xps))
4	2, 3	sylibr 200	1 |- ((A.xph -> A.xps) -> E.x(ph -> ps))

Syntax hints:   -> wi 3  A.wal 954  E.wex 980

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-4 973  ax-5o 975

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981

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