Theorem mtbid 597

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 147	. 2 |- ( ph -> ( ch -> ps ) )
4	1, 3	mtod 589	1 |- ( ph -> -. ch )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  sylnib  601  eqneltrrd  2134  neleqtrd  2135  eueq3dc  2715  efrirr  4090  nqnq0pi  6536  zdclt  8318  frec2uzf1od  9192  expnegap0  9263