Theorem mpgbi 987

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 151	. 2 |- (A.xph -> ps)
3		mpgbi.2	. 2 |- ph
4	2, 3	mpg 986	1 |- ps

Syntax hints:   <-> wb 146  A.wal 954

This theorem is referenced by:  nex 1101  exan 1106  nalset 2712  ac4 4750  ac8 4763  ackm 4782

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

This theorem depends on definitions:  df-bi 147

Copyright terms: Public domain