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Theorem mtbird 292
Description: A deduction from a biconditional, similar to modus tollens. (Contributed by NM, 10-May-1994.)
Hypotheses
Ref Expression
mtbird.min (φ → ¬ χ)
mtbird.maj (φ → (ψχ))
Assertion
Ref Expression
mtbird (φ → ¬ ψ)

Proof of Theorem mtbird
StepHypRef Expression
1 mtbird.min . 2 (φ → ¬ χ)
2 mtbird.maj . . 3 (φ → (ψχ))
32biimpd 198 . 2 (φ → (ψχ))
41, 3mtod 168 1 (φ → ¬ ψ)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 176
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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  6278  nnc3p1n3p2  6280  nchoicelem1  6289  nchoicelem2  6290  nchoicelem14  6302
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