Theorem ax9v 2117

Description: Weakened version of ax-9 2116, with a disjoint variable condition on 𝑥, 𝑦. This should be the only proof referencing ax-9 2116, and it should be referenced only by its two weakened versions ax9v1 2118 and ax9v2 2119, from which ax-9 2116 is then rederived as ax9 2120, which shows that either ax9v 2117 or the conjunction of ax9v1 2118 and ax9v2 2119 is sufficient. (Contributed by BJ, 7-Dec-2020.) Use ax9 2120 instead. (New usage is discouraged.)

Assertion

Ref	Expression
ax9v	⊢ (𝑥 = 𝑦 → (𝑧 ∈ 𝑥 → 𝑧 ∈ 𝑦))

Distinct variable group:   𝑥,𝑦

Proof of Theorem ax9v

Step	Hyp	Ref	Expression
1		ax-9 2116	1 ⊢ (𝑥 = 𝑦 → (𝑧 ∈ 𝑥 → 𝑧 ∈ 𝑦))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-9 2116

This theorem is referenced by:  ax9v1  2118  ax9v2  2119