Theorem ninba 575

Description: Miscellaneous inference relating falsehoods.

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 566	. 2 ⊢ (¬ ψ → ((χ ∧ ψ) ↔ ¬ φ))
3	2	bicomd 399	1 ⊢ (¬ ψ → (¬ φ ↔ (χ ∧ ψ)))

Syntax hints:  ¬ wn 1   → wi 2   ↔ wb 127   ∧ wa 196

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

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