Theorem mtbii 678

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 158	. 2 |- ( ph -> ( ch -> ps ) )
4	1, 3	mtoi 668	1 |- ( ph -> -. ch )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 617  ax-in2 618

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  onsucelsucexmid  4626  nntri2  6657  nntri3  6660  nndceq  6662  inffiexmid  7091  genpdisj  7733  ltposr  7973  hashennn  11032  fsumsplit  11958  sumsplitdc  11983  fprodm1  12149  m1dvdsndvds  12811