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Mirrors > Home > MPE Home > Th. List > alfal | Structured version Visualization version GIF version |
Description: For all sets, ¬ ⊥ is true. (Contributed by Anthony Hart, 13-Sep-2011.) |
Ref | Expression |
---|---|
alfal | ⊢ ∀𝑥 ¬ ⊥ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fal 1553 | . 2 ⊢ ¬ ⊥ | |
2 | 1 | ax-gen 1798 | 1 ⊢ ∀𝑥 ¬ ⊥ |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∀wal 1537 ⊥wfal 1551 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 |
This theorem depends on definitions: df-bi 206 df-tru 1542 df-fal 1552 |
This theorem is referenced by: nalfal 34592 |
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