Theorem mpbidi 231

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 219	. 2 |- ( ph -> ( ps -> ch ) )
4	1, 3	sylcom 30	1 |- ( th -> ( ph -> ch ) )

Syntax hints:   -> wi 4   <-> wb 196

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197

This theorem is referenced by:  tpid3gOLD  4306  ralxfr2d  4882  ovmpt4g  6783  ov3  6797  omeulem2  7663  domtriomlem  9264  nsmallnq  9799  bposlem1  25009  pntrsumbnd  25255  mptsnunlem  33185  poimirlem27  33436  frege92  38249  nzss  38516