Theorem ninba 927

Description: Miscellaneous inference relating falsehoods. (Contributed by NM, 31-Mar-1994.)

Hypothesis

Ref	Expression
ninba.1	⊢ φ

Assertion

Ref	Expression
ninba	⊢ (¬ ψ → (¬ φ ↔ (χ ∧ ψ)))

Proof of Theorem ninba

Step	Hyp	Ref	Expression
1		ninba.1	. . 3 ⊢ φ
2	1	niabn 917	. 2 ⊢ (¬ ψ → ((χ ∧ ψ) ↔ ¬ φ))
3	2	bicomd 192	1 ⊢ (¬ ψ → (¬ φ ↔ (χ ∧ 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: (None)