Theorem eqvrelsymrel 37464

Description: An equivalence relation is symmetric. (Contributed by Peter Mazsa, 29-Dec-2021.)

Assertion

Ref	Expression
eqvrelsymrel	⊢ ( EqvRel 𝑅 → SymRel 𝑅)

Proof of Theorem eqvrelsymrel

Step	Hyp	Ref	Expression
1		df-eqvrel 37450	. 2 ⊢ ( EqvRel 𝑅 ↔ ( RefRel 𝑅 ∧ SymRel 𝑅 ∧ TrRel 𝑅))
2	1	simp2bi 1146	1 ⊢ ( EqvRel 𝑅 → SymRel 𝑅)

Syntax hints:   → wi 4   RefRel wrefrel 37044   SymRel wsymrel 37050   TrRel wtrrel 37053   EqvRel weqvrel 37055

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-an 397  df-3an 1089  df-eqvrel 37450

This theorem is referenced by:  eqvrelim  37466  eqvrelsym  37470