Theorem pm5.35

Description: Theorem *5.35 of WhiteheadRussell p. 125. Closed form of 2thd . (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm5.35	⊢ ( ( ( 𝜑 → 𝜓 ) ∧ ( 𝜑 → 𝜒 ) ) → ( 𝜑 → ( 𝜓 ↔ 𝜒 ) ) )

Proof

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