Theorem ax9v2 2122

Description: Second of two weakened versions of ax9v 2120, with an extra disjoint variable condition on 𝑦, 𝑧 see comments there. (Contributed by BJ, 7-Dec-2020.)

Assertion

Ref	Expression
ax9v2	⊢ (𝑥 = 𝑦 → (𝑧 ∈ 𝑥 → 𝑧 ∈ 𝑦))

Distinct variable groups:   𝑥,𝑦   𝑦,𝑧

Proof of Theorem ax9v2

Step	Hyp	Ref	Expression
1		ax9v 2120	1 ⊢ (𝑥 = 𝑦 → (𝑧 ∈ 𝑥 → 𝑧 ∈ 𝑦))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-9 2119

This theorem is referenced by:  ax9  2123  dtruALT2  5345  dtruOLD  5421