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Theorem pm5.19 622
Description: Theorem *5.19 of [WhiteheadRussell] p. 124. (Contributed by NM, 3-Jan-2005.) (Revised by Mario Carneiro, 31-Jan-2015.)
Assertion
Ref Expression
pm5.19 ¬ (𝜑 ↔ ¬ 𝜑)

Proof of Theorem pm5.19
StepHypRef Expression
1 bi1 111 . . . 4 ((𝜑 ↔ ¬ 𝜑) → (𝜑 → ¬ 𝜑))
21pm2.01d 548 . . 3 ((𝜑 ↔ ¬ 𝜑) → ¬ 𝜑)
3 id 19 . . 3 ((𝜑 ↔ ¬ 𝜑) → (𝜑 ↔ ¬ 𝜑))
42, 3mpbird 156 . 2 ((𝜑 ↔ ¬ 𝜑) → 𝜑)
54, 2pm2.65i 568 1 ¬ (𝜑 ↔ ¬ 𝜑)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  pm5.16  737  pclem6  1265  pm5.18im  1276  ru  2763
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