Theorem pm5.19 706

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		biimp 118	. . . 4 ⊢ ((𝜑 ↔ ¬ 𝜑) → (𝜑 → ¬ 𝜑))
2	1	pm2.01d 618	. . 3 ⊢ ((𝜑 ↔ ¬ 𝜑) → ¬ 𝜑)
3		id 19	. . 3 ⊢ ((𝜑 ↔ ¬ 𝜑) → (𝜑 ↔ ¬ 𝜑))
4	2, 3	mpbird 167	. 2 ⊢ ((𝜑 ↔ ¬ 𝜑) → 𝜑)
5	4, 2	pm2.65i 639	1 ⊢ ¬ (𝜑 ↔ ¬ 𝜑)

Syntax hints:  ¬ wn 3   ↔ wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  pm5.16  828  pclem6  1374  pm5.18im  1385  ru  2963  canth  5831  exmidonfinlem  7194