Theorem pm5.19 391

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 264	. 2 ⊢ (𝜑 ↔ 𝜑)
2		pm5.18 384	. 2 ⊢ ((𝜑 ↔ 𝜑) ↔ ¬ (𝜑 ↔ ¬ 𝜑))
3	1, 2	mpbi 233	1 ⊢ ¬ (𝜑 ↔ ¬ 𝜑)

This proof depends on syntax axioms:  ¬ wn 3   ↔ wb 209

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210

This theorem is used by:  xorexmid  1557  ru0  2165  notsep  5336  pwfseqlem1  10654  bisym1  36963  rusbcALT  45181