Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > falbifal | Structured version Visualization version GIF version |
Description: A ↔ identity. (Contributed by Anthony Hart, 22-Oct-2010.) (Proof shortened by Andrew Salmon, 13-May-2011.) |
Ref | Expression |
---|---|
falbifal | ⊢ ((⊥ ↔ ⊥) ↔ ⊤) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | biid 251 | . 2 ⊢ (⊥ ↔ ⊥) | |
2 | 1 | bitru 1496 | 1 ⊢ ((⊥ ↔ ⊥) ↔ ⊤) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 196 ⊤wtru 1484 ⊥wfal 1488 |
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 197 df-tru 1486 |
This theorem is referenced by: falxorfal 1531 |
Copyright terms: Public domain | W3C validator |