Theorem ax9v1 2158

Description: First of two weakened versions of ax9v 2157, with an extra disjoint variable condition on 𝑥, 𝑧, see comments there. (Contributed by BJ, 7-Dec-2020.)

Assertion

Ref	Expression
ax9v1	⊢ (𝑥 = 𝑦 → (𝑧 ∈ 𝑥 → 𝑧 ∈ 𝑦))

Distinct variable groups:   𝑥,𝑦   𝑥,𝑧

Proof of Theorem ax9v1

Step	Hyp	Ref	Expression
1		ax9v 2157	1 ⊢ (𝑥 = 𝑦 → (𝑧 ∈ 𝑥 → 𝑧 ∈ 𝑦))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-9 2156

This theorem is used by:  ax9  2160  exexneq  5421  sn-exelALT  43031