Theorem pm5.19 349

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 227	. 2 ⊢ (φ ↔ φ)
2		pm5.18 345	. 2 ⊢ ((φ ↔ φ) ↔ ¬ (φ ↔ ¬ φ))
3	1, 2	mpbi 199	1 ⊢ ¬ (φ ↔ ¬ φ)

This proof depends on syntax axioms:  ¬ wn 3   ↔ wb 176

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

This proof depends on definitions:  df-bi 177

This theorem is used by:  ru  3046  necompl  3545  nenpw1pwlem2  6086