Theorem eqvrelsymrel 39392

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 39378	. 2 ⊢ ( EqvRel 𝑅 ↔ ( RefRel 𝑅 ∧ SymRel 𝑅 ∧ TrRel 𝑅))
2	1	simp2bi 1164	1 ⊢ ( EqvRel 𝑅 → SymRel 𝑅)

This proof depends on syntax axioms:   → wi 4   RefRel wrefrel 38898   SymRel wsymrel 38904   TrRel wtrrel 38907   EqvRel weqvrel 38909

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105  df-eqvrel 39378

This theorem is used by:  eqvrelim  39394  eqvrelsym  39398