Theorem equeuclr 2042

Description: Commuted version of equeucl 2043 (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 2041	. 2 ⊢ (𝑧 = 𝑥 → (𝑦 = 𝑧 → 𝑦 = 𝑥))
2	1	equcoms 2039	1 ⊢ (𝑥 = 𝑧 → (𝑦 = 𝑧 → 𝑦 = 𝑥))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027

This theorem depends on definitions:  df-bi 209  df-an 400  df-ex 1799

This theorem is referenced by:  equeucl  2043  equequ2  2045  ax13b  2051  aevlem0  2075  axc15  2452  euequ  2623  axprlem3  5379  exneq  5400