Metamath Proof Explorer


Theorem eceq2d

Description: Equality theorem for the A -coset and B -coset of C , deduction version. (Contributed by Peter Mazsa, 23-Apr-2021)

Ref Expression
Hypothesis eceq2d.1 φA=B
Assertion eceq2d φCA=CB

Proof

Step Hyp Ref Expression
1 eceq2d.1 φA=B
2 eceq2 A=BCA=CB
3 1 2 syl φCA=CB