Theorem biorfi 552

Description: A wff is equivalent to its disjunction with falsehood.

Hypothesis

Ref	Expression
biorfi.1	⊢ ¬ φ

Assertion

Ref	Expression
biorfi	⊢ (ψ ↔ (ψ ∨ φ))

Proof of Theorem biorfi

Step	Hyp	Ref	Expression
1		biorfi.1	. . 3 ⊢ ¬ φ
2		biorf 551	. . 3 ⊢ (¬ φ → (ψ ↔ (φ ∨ ψ)))
3	1, 2	ax-mp 6	. 2 ⊢ (ψ ↔ (φ ∨ ψ))
4		orcom 209	. 2 ⊢ ((φ ∨ ψ) ↔ (ψ ∨ φ))
5	3, 4	bitr 151	1 ⊢ (ψ ↔ (ψ ∨ φ))

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

This theorem is referenced by:  un0 1721  opthprc 2457  imadif 2714

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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