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 = 𝑡𝜑 ) ) )

Proof

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