Theorem pm5.19 386

Description: Theorem *5.19 of [WhiteheadRussell] p. 124. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm5.19	⊢ ¬ (𝜑 ↔ ¬ 𝜑)

Proof of Theorem pm5.19

Step	Hyp	Ref	Expression
1		biid 261	. 2 ⊢ (𝜑 ↔ 𝜑)
2		pm5.18 381	. 2 ⊢ ((𝜑 ↔ 𝜑) ↔ ¬ (𝜑 ↔ ¬ 𝜑))
3	1, 2	mpbi 230	1 ⊢ ¬ (𝜑 ↔ ¬ 𝜑)

Syntax hints:  ¬ wn 3   ↔ wb 206

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207

This theorem is referenced by:  xorexmid  1527  ru0  2127  ruOLD  3787  notzfaus  5363  pwfseqlem1  10698  bisym1  36420  rusbcALT  44458