Theorem mtbii 632

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 156	. 2 |- ( ph -> ( ch -> ps ) )
4	1, 3	mtoi 623	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 577  ax-in2 578

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  onsucelsucexmid  4301  nntri2  6158  nntri3  6161  nndceq  6163  inffiexmid  6457  genpdisj  6827  ltposr  7054  hashennn  9856