Theorem axc16gb

Description: Biconditional strengthening of axc16g . (Contributed by NM, 15-May-1993)

	Ref	Expression
Assertion	axc16gb	⊢ ( ∀ 𝑥 𝑥 = 𝑦 → ( 𝜑 ↔ ∀ 𝑧 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		axc16g	⊢ ( ∀ 𝑥 𝑥 = 𝑦 → ( 𝜑 → ∀ 𝑧 𝜑 ) )
2		sp	⊢ ( ∀ 𝑧 𝜑 → 𝜑 )
3	1 2	impbid1	⊢ ( ∀ 𝑥 𝑥 = 𝑦 → ( 𝜑 ↔ ∀ 𝑧 𝜑 ) )