Metamath Proof Explorer


Theorem equeucl

Description: Equality is a left-Euclidean binary relation. (Right-Euclideanness is stated in ax-7 .) Curried (exported) form of equtr2 . (Contributed by BJ, 11-Apr-2021)

Ref Expression
Assertion equeucl
|- ( x = z -> ( y = z -> x = y ) )

Proof

Step Hyp Ref Expression
1 equeuclr
 |-  ( y = z -> ( x = z -> x = y ) )
2 1 com12
 |-  ( x = z -> ( y = z -> x = y ) )