Theorem pm4.61 415

Description: Theorem *4.61 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm4.61	⊢ (¬ (φ → ψ) ↔ (φ ∧ ¬ ψ))

Proof of Theorem pm4.61

Step	Hyp	Ref	Expression
1		annim 414	. 2 ⊢ ((φ ∧ ¬ ψ) ↔ ¬ (φ → ψ))
2	1	bicomi 193	1 ⊢ (¬ (φ → ψ) ↔ (φ ∧ ¬ ψ))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 176   ∧ wa 358

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 177  df-an 360

This theorem is referenced by:  pm4.65  416  npss  3380  difin  3493