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Mirrors > Home > MPE Home > Th. List > nfnth | Structured version Visualization version GIF version |
Description: No variable is (effectively) free in a non-theorem. (Contributed by Mario Carneiro, 6-Dec-2016.) df-nf 1701 changed. (Revised by Wolf Lammen, 12-Sep-2021.) |
Ref | Expression |
---|---|
nfnth.1 | ⊢ ¬ 𝜑 |
Ref | Expression |
---|---|
nfnth | ⊢ Ⅎ𝑥𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfntht2 1711 | . 2 ⊢ (∀𝑥 ¬ 𝜑 → Ⅎ𝑥𝜑) | |
2 | nfnth.1 | . 2 ⊢ ¬ 𝜑 | |
3 | 1, 2 | mpg 1715 | 1 ⊢ Ⅎ𝑥𝜑 |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 Ⅎwnf 1699 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 |
This theorem depends on definitions: df-bi 196 df-or 384 df-ex 1696 df-nf 1701 |
This theorem is referenced by: nffal 1723 nd1 9288 nd2 9289 |
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