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Theorem pm3.37 822
Description: Theorem *3.37 (Transp) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm3.37 (((𝜑𝜓) → 𝜒) → ((𝜑 ∧ ¬ 𝜒) → ¬ 𝜓))

Proof of Theorem pm3.37
StepHypRef Expression
1 pm3.3 257 . . 3 (((𝜑𝜓) → 𝜒) → (𝜑 → (𝜓𝜒)))
2 con3 604 . . 3 ((𝜓𝜒) → (¬ 𝜒 → ¬ 𝜓))
31, 2syl6 33 . 2 (((𝜑𝜓) → 𝜒) → (𝜑 → (¬ 𝜒 → ¬ 𝜓)))
43impd 251 1 (((𝜑𝜓) → 𝜒) → ((𝜑 ∧ ¬ 𝜒) → ¬ 𝜓))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578
This theorem is referenced by:  ndvdssub  10708
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