Theorem mtbii 674

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 664	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 614  ax-in2 615

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  onsucelsucexmid  4531  nntri2  6497  nntri3  6500  nndceq  6502  inffiexmid  6908  genpdisj  7524  ltposr  7764  hashennn  10762  fsumsplit  11417  sumsplitdc  11442  fprodm1  11608  m1dvdsndvds  12250