Theorem ax12dgen

Description: Degenerate instance of ax-12 where bundled variables x and y have a common substitution. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 13-Apr-2017)

	Ref	Expression
Assertion	ax12dgen	⊢ ( 𝑥 = 𝑥 → ( ∀ 𝑥 𝜑 → ∀ 𝑥 ( 𝑥 = 𝑥 → 𝜑 ) ) )

Proof

Step	Hyp	Ref	Expression
1		ala1	⊢ ( ∀ 𝑥 𝜑 → ∀ 𝑥 ( 𝑥 = 𝑥 → 𝜑 ) )
2	1	a1i	⊢ ( 𝑥 = 𝑥 → ( ∀ 𝑥 𝜑 → ∀ 𝑥 ( 𝑥 = 𝑥 → 𝜑 ) ) )