Theorem mtbid 629

Description: A deduction from a biconditional, similar to modus tollens. (Contributed by NM, 26-Nov-1995.)

Hypotheses

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

Assertion

Ref	Expression
mtbid	|- ( ph -> -. ch )

Proof of Theorem mtbid

Step	Hyp	Ref	Expression
1		mtbid.min	. 2 |- ( ph -> -. ps )
2		mtbid.maj	. . 3 |- ( ph -> ( ps <-> ch ) )
3	2	biimprd 156	. 2 |- ( ph -> ( ch -> ps ) )
4	1, 3	mtod 621	1 |- ( ph -> -. ch )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 576  ax-in2 577

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  sylnib  633  eqneltrrd  2175  neleqtrd  2176  eueq3dc  2766  efrirr  4108  nqnq0pi  6628  zdclt  8425  frec2uzf1od  9408  expnegap0  9484  ibcval5  9690  rpdvds  10481  oddpwdclemodd  10550