Theorem ax8v1 2150

Description: First of two weakened versions of ax8v 2149, 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 2149	1 ⊢ (𝑥 = 𝑦 → (𝑥 ∈ 𝑧 → 𝑦 ∈ 𝑧))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-8 2148

This theorem is used by:  ax8  2152  el  5421  bj-cleljusti  37359