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Theorem mtbii 640
 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 631 1 (𝜑 → ¬ 𝜒)
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 104 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 584  ax-in2 585 This theorem depends on definitions:  df-bi 116 This theorem is referenced by:  onsucelsucexmid  4383  nntri2  6320  nntri3  6323  nndceq  6325  inffiexmid  6729  genpdisj  7232  ltposr  7459  hashennn  10367  fsumsplit  11015  sumsplitdc  11040
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