Theorem biortn 951

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 143	. 2 ⊢ (𝜑 → ¬ ¬ 𝜑)
2		biorf 950	. 2 ⊢ (¬ ¬ 𝜑 → (𝜓 ↔ (¬ 𝜑 ∨ 𝜓)))
3	1, 2	syl 18	1 ⊢ (𝜑 → (𝜓 ↔ (¬ 𝜑 ∨ 𝜓)))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ↔ wb 209   ∨ wo 861

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-or 862

This theorem is used by:  oranabs  1015  xrdifh  33197  ballotlemfc0  34950  ballotlemfcc  34951  topdifinfindis  38051  topdifinffinlem  38052  4atlem3a  40431  4atlem3b  40432  ntrneineine1lem  44870