Metamath Proof Explorer


Theorem equcomd

Description: Deduction form of equcom , symmetry of equality. For the versions for classes, see eqcom and eqcomd . (Contributed by BJ, 6-Oct-2019)

Ref Expression
Hypothesis equcomd.1 ⊢ φ → x = y
Assertion equcomd ⊢ φ → y = x

Proof

Step Hyp Ref Expression
1 equcomd.1 ⊢ φ → x = y
2 equcom ⊢ x = y ↔ y = x
3 1 2 sylib ⊢ φ → y = x