Theorem biortn 395

Description: A wff is equivalent to its negated disjunction with falsehood. (Contributed by NM, 9-Jul-2012.)

Assertion

Ref	Expression
biortn	⊢ (φ → (ψ ↔ (¬ φ ∨ ψ)))

Proof of Theorem biortn

Step	Hyp	Ref	Expression
1		notnot1 114	. 2 ⊢ (φ → ¬ ¬ φ)
2		biorf 394	. 2 ⊢ (¬ ¬ φ → (ψ ↔ (¬ φ ∨ ψ)))
3	1, 2	syl 15	1 ⊢ (φ → (ψ ↔ (¬ φ ∨ ψ)))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 176   ∨ wo 357

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-or 359

This theorem is referenced by:  oranabs  829