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Mirrors > Home > MPE Home > Th. List > nffal | Structured version Visualization version GIF version |
Description: The false constant has no free variables (see nftru 1730). (Contributed by BJ, 6-May-2019.) |
Ref | Expression |
---|---|
nffal | ⊢ Ⅎ𝑥⊥ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fal 1490 | . 2 ⊢ ¬ ⊥ | |
2 | 1 | nfnth 1728 | 1 ⊢ Ⅎ𝑥⊥ |
Colors of variables: wff setvar class |
Syntax hints: ⊥wfal 1488 Ⅎwnf 1708 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 |
This theorem depends on definitions: df-bi 197 df-or 385 df-tru 1486 df-fal 1489 df-ex 1705 df-nf 1710 |
This theorem is referenced by: (None) |
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