Theorem biort 866

Description: A wff disjoined with truth is true. (Contributed by NM, 23-May-1999.)

Assertion

Ref	Expression
biort	⊢ (φ → (φ ↔ (φ ∨ ψ)))

Proof of Theorem biort

Step	Hyp	Ref	Expression
1		orc 374	. 2 ⊢ (φ → (φ ∨ ψ))
2		ax-1 6	. 2 ⊢ (φ → ((φ ∨ ψ) → φ))
3	1, 2	impbid2 195	1 ⊢ (φ → (φ ↔ (φ ∨ ψ)))

Syntax hints:   → 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:  pm5.55  867