Theorem equcomd 1717

Description: Deduction form of equcom 1716, symmetry of equality. For the versions for classes, see eqcom 2189 and eqcomd 2193. (Contributed by BJ, 6-Oct-2019.)

Hypothesis

Ref	Expression
equcomd.1	⊢ (𝜑 → 𝑥 = 𝑦)

Assertion

Ref	Expression
equcomd	⊢ (𝜑 → 𝑦 = 𝑥)

Proof of Theorem equcomd

Step	Hyp	Ref	Expression
1		equcomd.1	. 2 ⊢ (𝜑 → 𝑥 = 𝑦)
2		equcom 1716	. 2 ⊢ (𝑥 = 𝑦 ↔ 𝑦 = 𝑥)
3	1, 2	sylib 122	1 ⊢ (𝜑 → 𝑦 = 𝑥)

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-gen 1459  ax-ie2 1504  ax-8 1514  ax-17 1536  ax-i9 1540

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  fisumcom2  11459  fprodcom2fi  11647  trirec0  15064