Theorem biort 780

Description: A wff is 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 674	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓))
2		ax-1 5	. 2 ⊢ (𝜑 → ((𝜑 ∨ 𝜓) → 𝜑))
3	1, 2	impbid2 142	1 ⊢ (𝜑 → (𝜑 ↔ (𝜑 ∨ 𝜓)))

Syntax hints:   → wi 4   ↔ wb 104   ∨ wo 670

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 671

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  pm5.55dc  863