Theorem biort 550

Description: A wff is disjoined with truth is true.

Assertion

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

Proof of Theorem biort

Step	Hyp	Ref	Expression
1		orc 225	. . 3 ⊢ (φ → (φ ∨ ψ))
2	1	a1d 14	. 2 ⊢ (φ → (φ → (φ ∨ ψ)))
3		ax-1 3	. 2 ⊢ (φ → ((φ ∨ ψ) → φ))
4	2, 3	impbid 397	1 ⊢ (φ → (φ ↔ (φ ∨ ψ)))

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

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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