Theorem equeuclr 1950

Description: Commuted version of equeucl 1951 (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 1949	. 2 |- ( z = x -> ( y = z -> y = x ) )
2	1	equcoms 1947	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 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705

This theorem is referenced by:  equeucl  1951  equequ2  1953  ax13b  1964  aevlem0  1980  equvini  2346  sbequi  2375  wl-ax8clv2  33381