Theorem eqvrelrefrel 39372

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

Assertion

Ref	Expression
eqvrelrefrel	⊢ ( EqvRel 𝑅 → RefRel 𝑅)

Proof of Theorem eqvrelrefrel

Step	Hyp	Ref	Expression
1		df-eqvrel 39359	. 2 ⊢ ( EqvRel 𝑅 ↔ ( RefRel 𝑅 ∧ SymRel 𝑅 ∧ TrRel 𝑅))
2	1	simp1bi 1163	1 ⊢ ( EqvRel 𝑅 → RefRel 𝑅)

This proof depends on syntax axioms:   → wi 4   RefRel wrefrel 38879   SymRel wsymrel 38885   TrRel wtrrel 38888   EqvRel weqvrel 38890

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 39359

This theorem is used by: (None)