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Mirrors > Home > ILE Home > Th. List > falantru | GIF version |
Description: A ∧ identity. (Contributed by David A. Wheeler, 23-Feb-2018.) |
Ref | Expression |
---|---|
falantru | ⊢ ((⊥ ∧ ⊤) ↔ ⊥) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 109 | . 2 ⊢ ((⊥ ∧ ⊤) → ⊥) | |
2 | falim 1367 | . 2 ⊢ (⊥ → (⊥ ∧ ⊤)) | |
3 | 1, 2 | impbii 126 | 1 ⊢ ((⊥ ∧ ⊤) ↔ ⊥) |
Colors of variables: wff set class |
Syntax hints: ∧ wa 104 ↔ 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 ax-in1 614 ax-in2 615 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-fal 1359 |
This theorem is referenced by: trubifal 1416 falxortru 1421 falxorfal 1422 |
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