Theorem mtbird 292

Description: A deduction from a biconditional, similar to modus tollens. (Contributed by NM, 10-May-1994.)

Hypotheses

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

Assertion

Ref	Expression
mtbird	|- (ph -> -. ps)

Proof of Theorem mtbird

Step	Hyp	Ref	Expression
1		mtbird.min	. 2 |- (ph -> -. ch)
2		mtbird.maj	. . 3 |- (ph -> (ps <-> ch))
3	2	biimpd 198	. 2 |- (ph -> (ps -> ch))
4	1, 3	mtod 168	1 |- (ph -> -. ps)

Syntax hints:  -. wn 3   -> wi 4   <-> wb 176

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8

This theorem depends on definitions:  df-bi 177

This theorem is referenced by:  eqneltrd  2446  neleqtrrd  2449  ltfinirr  4457  nnadjoin  4520  vfin1cltv  4547  fvun1  5379  nnc3n3p1  6276  nnc3p1n3p2  6278  nchoicelem1  6287  nchoicelem2  6288  nchoicelem14  6300