Mathbox for Peter Mazsa |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > eqvrelrefrel | Structured version Visualization version GIF version |
Description: An equivalence relation is reflexive. (Contributed by Peter Mazsa, 29-Dec-2021.) |
Ref | Expression |
---|---|
eqvrelrefrel | ⊢ ( EqvRel 𝑅 → RefRel 𝑅) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-eqvrel 36698 | . 2 ⊢ ( EqvRel 𝑅 ↔ ( RefRel 𝑅 ∧ SymRel 𝑅 ∧ TrRel 𝑅)) | |
2 | 1 | simp1bi 1144 | 1 ⊢ ( EqvRel 𝑅 → RefRel 𝑅) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 RefRel wrefrel 36339 SymRel wsymrel 36345 TrRel wtrrel 36348 EqvRel weqvrel 36350 |
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 1088 df-eqvrel 36698 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |