Theorem albidv

Description: Formula-building rule for universal quantifier (deduction form). See also albidh and albid . (Contributed by NM, 26-May-1993)

	Ref	Expression
Hypothesis	albidv.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
Assertion	albidv	⊢ ( 𝜑 → ( ∀ 𝑥 𝜓 ↔ ∀ 𝑥 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		albidv.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
2		ax-5	⊢ ( 𝜑 → ∀ 𝑥 𝜑 )
3	2 1	albidh	⊢ ( 𝜑 → ( ∀ 𝑥 𝜓 ↔ ∀ 𝑥 𝜒 ) )