Theorem ax8v1 2112

Description: First of two weakened versions of ax8v 2111, with an extra disjoint variable condition on 𝑥, 𝑧, see comments there. (Contributed by BJ, 7-Dec-2020.)

Assertion

Ref	Expression
ax8v1	⊢ (𝑥 = 𝑦 → (𝑥 ∈ 𝑧 → 𝑦 ∈ 𝑧))

Distinct variable groups:   𝑥,𝑦   𝑥,𝑧

Proof of Theorem ax8v1

Step	Hyp	Ref	Expression
1		ax8v 2111	1 ⊢ (𝑥 = 𝑦 → (𝑥 ∈ 𝑧 → 𝑦 ∈ 𝑧))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-8 2110

This theorem is referenced by:  ax8  2114  bj-cleljusti  34788