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Metamath Proof Explorer

Theorem bj-ax12v

Description: A weaker form of ax-12 and ax12v , namely the generalization over x of the latter. In this statement, all occurrences of x are bound. (Contributed by BJ, 26-Dec-2020) (Proof modification is discouraged.)

		Ref	Expression
	Assertion	bj-ax12v	⊢ ∀ 𝑥 ( 𝑥 = 𝑡 → ( 𝜑 → ∀ 𝑥 ( 𝑥 = 𝑡 → 𝜑 ) ) )

Proof

Step	Hyp	Ref	Expression
1		ax12v	⊢ ( 𝑥 = 𝑡 → ( 𝜑 → ∀ 𝑥 ( 𝑥 = 𝑡 → 𝜑 ) ) )
2	1	ax-gen	⊢ ∀ 𝑥 ( 𝑥 = 𝑡 → ( 𝜑 → ∀ 𝑥 ( 𝑥 = 𝑡 → 𝜑 ) ) )