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Theorem pm5.16 773
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 pm5.19 657 . 2 ¬ (𝜓 ↔ ¬ 𝜓)
2 simpl 107 . . 3 (((𝜑𝜓) ∧ (𝜑 ↔ ¬ 𝜓)) → (𝜑𝜓))
3 simpr 108 . . 3 (((𝜑𝜓) ∧ (𝜑 ↔ ¬ 𝜓)) → (𝜑 ↔ ¬ 𝜓))
42, 3bitr3d 188 . 2 (((𝜑𝜓) ∧ (𝜑 ↔ ¬ 𝜓)) → (𝜓 ↔ ¬ 𝜓))
51, 4mto 623 1 ¬ ((𝜑𝜓) ∧ (𝜑 ↔ ¬ 𝜓))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wa 102  wb 103
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 579  ax-in2 580
This theorem depends on definitions:  df-bi 115
This theorem is referenced by: (None)
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