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Theorem mtbii 609
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 151 . 2 (𝜑 → (𝜒𝜓))
41, 3mtoi 600 1 (𝜑 → ¬ 𝜒)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  onsucelsucexmid  4282  nntri2  6103  nntri3  6105  nndceq  6107  genpdisj  6678  ltposr  6905
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