Theorem mpbidi 151

Description: A deduction from a biconditional, related to modus ponens. (Contributed by NM, 9-Aug-1994.)

Hypotheses

Ref	Expression
mpbidi.min	|- ( th -> ( ph -> ps ) )
mpbidi.maj	|- ( ph -> ( ps <-> ch ) )

Assertion

Ref	Expression
mpbidi	|- ( th -> ( ph -> ch ) )

Proof of Theorem mpbidi

Step	Hyp	Ref	Expression
1		mpbidi.min	. 2 |- ( th -> ( ph -> ps ) )
2		mpbidi.maj	. . 3 |- ( ph -> ( ps <-> ch ) )
3	2	biimpd 144	. 2 |- ( ph -> ( ps -> ch ) )
4	1, 3	sylcom 28	1 |- ( th -> ( ph -> ch ) )

Syntax hints:   -> wi 4   <-> wb 105

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

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  tpid3g  3707  ralxfr2d  4463  rexxfr2d  4464  ovmpt4g  5994  ovi3  6008  bj-inf2vnlem1  14582