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Metamath Proof Explorer

Theorem eceq2i

Description: Equality theorem for the A -coset and B -coset of C , inference version. (Contributed by Peter Mazsa, 11-May-2021)

Ref Expression
Hypothesis eceq2i.1 ⊢ A = B
Assertion eceq2i ⊢ C A = C B

Proof

Step Hyp Ref Expression
1 eceq2i.1 ⊢ A = B
2 eceq2 ⊢ A = B → C A = C B
3 1 2 ax-mp ⊢ C A = C B