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Theorem mtbii 675
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 158 . 2 (𝜑 → (𝜒𝜓))
41, 3mtoi 665 1 (𝜑 → ¬ 𝜒)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 105
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  onsucelsucexmid  4562  nntri2  6547  nntri3  6550  nndceq  6552  inffiexmid  6962  genpdisj  7583  ltposr  7823  hashennn  10851  fsumsplit  11550  sumsplitdc  11575  fprodm1  11741  m1dvdsndvds  12386
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