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Mirrors > Home > ILE Home > Th. List > nfnth | GIF version |
Description: No variable is (effectively) free in a non-theorem. (Contributed by Mario Carneiro, 6-Dec-2016.) |
Ref | Expression |
---|---|
nfnth.1 | ⊢ ¬ 𝜑 |
Ref | Expression |
---|---|
nfnth | ⊢ Ⅎ𝑥𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfnth.1 | . . 3 ⊢ ¬ 𝜑 | |
2 | 1 | pm2.21i 641 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) |
3 | 2 | nfi 1455 | 1 ⊢ Ⅎ𝑥𝜑 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ∀wal 1346 Ⅎwnf 1453 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in2 610 ax-gen 1442 |
This theorem depends on definitions: df-bi 116 df-nf 1454 |
This theorem is referenced by: (None) |
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