Theorem equeuclr 2055

Description: Commuted version of equeucl 2056 (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 2054	. 2 ⊢ (𝑧 = 𝑥 → (𝑦 = 𝑧 → 𝑦 = 𝑥))
2	1	equcoms 2052	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 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1812

This theorem is used by:  equeucl  2056  equequ2  2058  ax13b  2064  aevlem0  2088  axc15  2451  euequ  2622  axprlem3  5386  exneq  5403