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Mirrors > Home > MPE Home > Th. List > falantru | Structured version Visualization version GIF version |
Description: A ∧ identity. (Contributed by Anthony Hart, 22-Oct-2010.) |
Ref | Expression |
---|---|
falantru | ⊢ ((⊥ ∧ ⊤) ↔ ⊥) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fal 1553 | . . 3 ⊢ ¬ ⊥ | |
2 | 1 | intnanr 488 | . 2 ⊢ ¬ (⊥ ∧ ⊤) |
3 | 2 | bifal 1555 | 1 ⊢ ((⊥ ∧ ⊤) ↔ ⊥) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 205 ∧ wa 396 ⊤wtru 1540 ⊥wfal 1551 |
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-tru 1542 df-fal 1552 |
This theorem is referenced by: (None) |
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