Theorem biortn 943

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		notnot 142	. 2 ⊢ (𝜑 → ¬ ¬ 𝜑)
2		biorf 942	. 2 ⊢ (¬ ¬ 𝜑 → (𝜓 ↔ (¬ 𝜑 ∨ 𝜓)))
3	1, 2	syl 17	1 ⊢ (𝜑 → (𝜓 ↔ (¬ 𝜑 ∨ 𝜓)))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 207   ∨ wo 853

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 208  df-or 854

This theorem is referenced by:  oranabs  1007  xrdifh  32872  ballotlemfc0  34677  ballotlemfcc  34678  topdifinfindis  37708  topdifinffinlem  37709  4atlem3a  40089  4atlem3b  40090  ntrneineine1lem  44528