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Theorem mtbii 663
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 157 . 2 (𝜑 → (𝜒𝜓))
41, 3mtoi 653 1 (𝜑 → ¬ 𝜒)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  onsucelsucexmid  4445  nntri2  6390  nntri3  6393  nndceq  6395  inffiexmid  6800  genpdisj  7343  ltposr  7583  hashennn  10538  fsumsplit  11188  sumsplitdc  11213
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