Theorem pm5.19 695

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

Step	Hyp	Ref	Expression
1		bi1 117	. . . 4 ⊢ ((𝜑 ↔ ¬ 𝜑) → (𝜑 → ¬ 𝜑))
2	1	pm2.01d 607	. . 3 ⊢ ((𝜑 ↔ ¬ 𝜑) → ¬ 𝜑)
3		id 19	. . 3 ⊢ ((𝜑 ↔ ¬ 𝜑) → (𝜑 ↔ ¬ 𝜑))
4	2, 3	mpbird 166	. 2 ⊢ ((𝜑 ↔ ¬ 𝜑) → 𝜑)
5	4, 2	pm2.65i 628	1 ⊢ ¬ (𝜑 ↔ ¬ 𝜑)

Syntax hints:  ¬ wn 3   ↔ 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 603  ax-in2 604

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  pm5.16  813  pclem6  1352  pm5.18im  1363  ru  2903  exmidonfinlem  7042