Theorem pm5.74rd

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

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

Proof

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