Theorem equeuclr 2058

Description: Commuted version of equeucl 2059 (equality is left-Euclidean). (Contributed by BJ, 12-Apr-2021.)

Assertion

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

Proof of Theorem equeuclr

Step	Hyp	Ref	Expression
1		equtrr 2057	. 2 ⊢ (𝑧 = 𝑥 → (𝑦 = 𝑧 → 𝑦 = 𝑥))
2	1	equcoms 2055	1 ⊢ (𝑥 = 𝑧 → (𝑦 = 𝑧 → 𝑦 = 𝑥))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1813

This theorem is used by:  equeucl  2059  equequ2  2061  ax13b  2067  aevlem0  2091  axc15  2454  euequ  2625  axprlem3  5392  exneq  5409