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Theorem pm5.16 798
Description: Theorem *5.16 of [WhiteheadRussell] p. 124. (Contributed by NM, 3-Jan-2005.) (Revised by Mario Carneiro, 31-Jan-2015.)
Assertion
Ref Expression
pm5.16 ¬ ((𝜑𝜓) ∧ (𝜑 ↔ ¬ 𝜓))

Proof of Theorem pm5.16
StepHypRef Expression
1 pm5.19 680 . 2 ¬ (𝜓 ↔ ¬ 𝜓)
2 simpl 108 . . 3 (((𝜑𝜓) ∧ (𝜑 ↔ ¬ 𝜓)) → (𝜑𝜓))
3 simpr 109 . . 3 (((𝜑𝜓) ∧ (𝜑 ↔ ¬ 𝜓)) → (𝜑 ↔ ¬ 𝜓))
42, 3bitr3d 189 . 2 (((𝜑𝜓) ∧ (𝜑 ↔ ¬ 𝜓)) → (𝜓 ↔ ¬ 𝜓))
51, 4mto 636 1 ¬ ((𝜑𝜓) ∧ (𝜑 ↔ ¬ 𝜓))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wa 103  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 588  ax-in2 589
This theorem depends on definitions:  df-bi 116
This theorem is referenced by: (None)
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