Theorem mpgbi 1452

Description: Modus ponens on biconditional combined with generalization. (Contributed by NM, 24-May-1994.) (Proof shortened by Stefan Allan, 28-Oct-2008.)

Hypotheses

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

Assertion

Ref	Expression
mpgbi	|- ps

Proof of Theorem mpgbi

Step	Hyp	Ref	Expression
1		mpgbi.2	. . 3 |- ph
2	1	ax-gen 1449	. 2 |- A. x ph
3		mpgbi.1	. 2 |- ( A. x ph <-> ps )
4	2, 3	mpbi 145	1 |- ps

Syntax hints:   <-> wb 105   A.wal 1351

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-gen 1449

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  nex  1500  exlimih  1593  exan  1693  abbii  2293  bj-ex  14553