Theorem mpgbi 685

Description: Modus ponens on biconditional combined with generalization.

Hypotheses

Ref	Expression
mpgbi.1	|- (A.xph <-> ps)
mpgbi.2	|- ph

Assertion

Ref	Expression
mpgbi	|- ps

Proof of Theorem mpgbi

Step	Hyp	Ref	Expression
1		mpgbi.1	. . 3 |- (A.xph <-> ps)
2	1	biimp 133	. 2 |- (A.xph -> ps)
3		mpgbi.2	. 2 |- ph
4	2, 3	mpg 684	1 |- ps

Syntax hints:   <-> wb 127  A.wal 672

This theorem is referenced by:  nex 779  exan 784  nalset 1482  ac4 3571  ac8 3579  ackm 3597

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

This theorem depends on definitions:  df-bi 128

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