Theorem albitr

Description: Theorem *10.301 in WhiteheadRussell p. 151. (Contributed by Andrew Salmon, 24-May-2011)

	Ref	Expression
Assertion	albitr	⊢ ( ( ∀ 𝑥 ( 𝜑 ↔ 𝜓 ) ∧ ∀ 𝑥 ( 𝜓 ↔ 𝜒 ) ) → ∀ 𝑥 ( 𝜑 ↔ 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		bitr	⊢ ( ( ( 𝜑 ↔ 𝜓 ) ∧ ( 𝜓 ↔ 𝜒 ) ) → ( 𝜑 ↔ 𝜒 ) )
2	1	alanimi	⊢ ( ( ∀ 𝑥 ( 𝜑 ↔ 𝜓 ) ∧ ∀ 𝑥 ( 𝜓 ↔ 𝜒 ) ) → ∀ 𝑥 ( 𝜑 ↔ 𝜒 ) )