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Theorem mtbid 597
Description: A deduction from a biconditional, similar to modus tollens. (Contributed by NM, 26-Nov-1995.)
Hypotheses
Ref Expression
mtbid.min (𝜑 → ¬ 𝜓)
mtbid.maj (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
mtbid (𝜑 → ¬ 𝜒)

Proof of Theorem mtbid
StepHypRef Expression
1 mtbid.min . 2 (𝜑 → ¬ 𝜓)
2 mtbid.maj . . 3 (𝜑 → (𝜓𝜒))
32biimprd 147 . 2 (𝜑 → (𝜒𝜓))
41, 3mtod 589 1 (𝜑 → ¬ 𝜒)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  sylnib  601  eqneltrrd  2134  neleqtrd  2135  eueq3dc  2712  efrirr  4084  nqnq0pi  6508  zdclt  8281  frec2uzf1od  9061  expnegap0  9132
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