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Theorem mtbid 581
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 573 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 529  ax-in2 530
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  sylnib  585  eqneltrrd  2107  neleqtrd  2108  eueq3dc  2683  nqnq0pi  6279
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