Theorem biorf 551

Description: A wff is equivalent to its disjunction with falsehood. Theorem *4.74 of [WhiteheadRussell] p. 121.

Assertion

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

Proof of Theorem biorf

Step	Hyp	Ref	Expression
1		biimt 549	. 2 ⊢ (¬ φ → (ψ ↔ (¬ φ → ψ)))
2		df-or 197	. 2 ⊢ ((φ ∨ ψ) ↔ (¬ φ → ψ))
3	1, 2	syl6bbr 416	1 ⊢ (¬ φ → (ψ ↔ (φ ∨ ψ)))

Syntax hints:  ¬ wn 1   → wi 2   ↔ wb 127   ∨ wo 195

This theorem is referenced by:  biorfi 552  19.33b 771  euorv 1025  unineq 1680  opthwiener 1914  iununi 2037  opthprc 2457

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-or 197  df-an 198

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