Theorem biorfd 38919

Description: A wff is equivalent to its disjunction with falsehood, deduction form. (Contributed by Peter Mazsa, 22-Aug-2023.)

Hypothesis

Ref	Expression
biorfd.1	⊢ (𝜑 → ¬ 𝜓)

Assertion

Ref	Expression
biorfd	⊢ (𝜑 → (𝜒 ↔ (𝜓 ∨ 𝜒)))

Proof of Theorem biorfd

Step	Hyp	Ref	Expression
1		biorfd.1	. 2 ⊢ (𝜑 → ¬ 𝜓)
2		biorf 950	. 2 ⊢ (¬ 𝜓 → (𝜒 ↔ (𝜓 ∨ 𝜒)))
3	1, 2	syl 18	1 ⊢ (𝜑 → (𝜒 ↔ (𝜓 ∨ 𝜒)))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ↔ wb 209   ∨ wo 861

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-or 862

This theorem is used by:  disjressuc2  39093