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Mirrors > Home > ILE Home > Th. List > truimfal | GIF version |
Description: A → identity. (Contributed by Anthony Hart, 22-Oct-2010.) (Proof shortened by Andrew Salmon, 13-May-2011.) |
Ref | Expression |
---|---|
truimfal | ⊢ ((⊤ → ⊥) ↔ ⊥) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tru 1357 | . . 3 ⊢ ⊤ | |
2 | 1 | a1bi 243 | . 2 ⊢ (⊥ ↔ (⊤ → ⊥)) |
3 | 2 | bicomi 132 | 1 ⊢ ((⊤ → ⊥) ↔ ⊥) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ↔ wb 105 ⊤wtru 1354 ⊥wfal 1358 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 |
This theorem depends on definitions: df-bi 117 df-tru 1356 |
This theorem is referenced by: trubifal 1416 |
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