Theorem ax9v1 2118

Description: First of two weakened versions of ax9v 2117, 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 2117	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:  ax9  2120  sn-el  40187  sn-dtru  40188