Theorem mtbii 599

Description: An inference from a biconditional, similar to modus tollens. (Contributed by NM, 27-Nov-1995.)

Hypotheses

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

Assertion

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

Proof of Theorem mtbii

Step	Hyp	Ref	Expression
1		mtbii.min	. 2 |- -. ps
2		mtbii.maj	. . 3 |- ( ph -> ( ps <-> ch ) )
3	2	biimprd 147	. 2 |- ( ph -> ( ch -> ps ) )
4	1, 3	mtoi 590	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:  onsucelsucexmid  4255  nntri2  6073  nntri3  6075  nndceq  6077  genpdisj  6621  ltposr  6848