Theorem logic1a

Description: Variant of logic1 . (Contributed by Zhi Wang, 30-Aug-2024)

	Ref	Expression
Hypotheses	pm4.71da.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
	logic1a.2	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜃 ↔ 𝜏 ) )
Assertion	logic1a	⊢ ( 𝜑 → ( ( 𝜓 → 𝜃 ) ↔ ( 𝜒 → 𝜏 ) ) )

Proof

Step	Hyp	Ref	Expression
1		pm4.71da.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
2		logic1a.2	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜃 ↔ 𝜏 ) )
3	2	ex	⊢ ( 𝜑 → ( 𝜓 → ( 𝜃 ↔ 𝜏 ) ) )
4	1 3	logic1	⊢ ( 𝜑 → ( ( 𝜓 → 𝜃 ) ↔ ( 𝜒 → 𝜏 ) ) )