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Mirrors > Home > ILE Home > Th. List > falbitru | GIF version |
Description: A ↔ identity. (Contributed by Anthony Hart, 22-Oct-2010.) (Proof shortened by Andrew Salmon, 13-May-2011.) |
Ref | Expression |
---|---|
falbitru | ⊢ ((⊥ ↔ ⊤) ↔ ⊥) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bicom 128 | . 2 ⊢ ((⊥ ↔ ⊤) ↔ (⊤ ↔ ⊥)) | |
2 | trubifal 1307 | . 2 ⊢ ((⊤ ↔ ⊥) ↔ ⊥) | |
3 | 1, 2 | bitri 173 | 1 ⊢ ((⊥ ↔ ⊤) ↔ ⊥) |
Colors of variables: wff set class |
Syntax hints: ↔ wb 98 ⊤wtru 1244 ⊥wfal 1248 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-fal 1249 |
This theorem is referenced by: (None) |
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