Theorem pm5.74da

Description: Distribution of implication over biconditional (deduction form). Variant of pm5.74d . (Contributed by NM, 4-May-2007)

	Ref	Expression
Hypothesis	pm5.74da.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 ↔ 𝜃 ) )
Assertion	pm5.74da	⊢ ( 𝜑 → ( ( 𝜓 → 𝜒 ) ↔ ( 𝜓 → 𝜃 ) ) )

Proof

Step	Hyp	Ref	Expression
1		pm5.74da.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 ↔ 𝜃 ) )
2	1	ex	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 ↔ 𝜃 ) ) )
3	2	pm5.74d	⊢ ( 𝜑 → ( ( 𝜓 → 𝜒 ) ↔ ( 𝜓 → 𝜃 ) ) )