Theorem ax7v1 2043

Description: First of two weakened versions of ax7v 2042, with an extra disjoint variable condition on 𝑥, 𝑧, see comments there. (Contributed by BJ, 7-Dec-2020.)

Assertion

Ref	Expression
ax7v1	⊢ (𝑥 = 𝑦 → (𝑥 = 𝑧 → 𝑦 = 𝑧))

Distinct variable groups:   𝑥,𝑦   𝑥,𝑧

Proof of Theorem ax7v1

Step	Hyp	Ref	Expression
1		ax7v 2042	1 ⊢ (𝑥 = 𝑦 → (𝑥 = 𝑧 → 𝑦 = 𝑧))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-7 2041

This theorem is used by:  equid  2045  ax7  2049  ax13  2410  dtruALT2  5346  exneq  5422