Theorem mtbid 632

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 624	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 579  ax-in2 580

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  sylnib  636  eqneltrrd  2184  neleqtrd  2185  eueq3dc  2787  efrirr  4171  fidcenumlemrks  6641  nqnq0pi  6976  zdclt  8794  frec2uzf1od  9778  expnegap0  9928  ibcval5  10136  zfz1isolemiso  10209  iseqcoll  10212  fisumss  10748  rpdvds  11174  oddpwdclemodd  11243