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Theorem mtbii 598
Description: An inference from a biconditional, similar to modus tollens. (Contributed by NM, 27-Nov-1995.)
Hypotheses
Ref Expression
mtbii.min ¬ ψ
mtbii.maj (φ → (ψχ))
Assertion
Ref Expression
mtbii (φ → ¬ χ)

Proof of Theorem mtbii
StepHypRef Expression
1 mtbii.min . 2 ¬ ψ
2 mtbii.maj . . 3 (φ → (ψχ))
32biimprd 147 . 2 (φ → (χψ))
41, 3mtoi 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:  onsucelsucexmid  4215  nntri2  6012  nntri3  6014  nndceq  6015  genpdisj  6506  ltposr  6691
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