Theorem pm5.74rd 277

Description: Distribution of implication over biconditional (deduction form). (Contributed by NM, 19-Mar-1997.)

Hypothesis

Ref	Expression
pm5.74rd.1	⊢ (𝜑 → ((𝜓 → 𝜒) ↔ (𝜓 → 𝜃)))

Assertion

Ref	Expression
pm5.74rd	⊢ (𝜑 → (𝜓 → (𝜒 ↔ 𝜃)))

Proof of Theorem pm5.74rd

Step	Hyp	Ref	Expression
1		pm5.74rd.1	. 2 ⊢ (𝜑 → ((𝜓 → 𝜒) ↔ (𝜓 → 𝜃)))
2		pm5.74 273	. 2 ⊢ ((𝜓 → (𝜒 ↔ 𝜃)) ↔ ((𝜓 → 𝜒) ↔ (𝜓 → 𝜃)))
3	1, 2	sylibr 237	1 ⊢ (𝜑 → (𝜓 → (𝜒 ↔ 𝜃)))

This proof depends on syntax axioms:   → wi 4   ↔ wb 209

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

This theorem is used by:  imbibiOLD  396  pm5.35  837  wl-dral1d  38214