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Mirrors > Home > ILE Home > Th. List > nfth | GIF version |
Description: No variable is (effectively) free in a theorem. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
hbth.1 | ⊢ 𝜑 |
Ref | Expression |
---|---|
nfth | ⊢ Ⅎ𝑥𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbth.1 | . . 3 ⊢ 𝜑 | |
2 | 1 | hbth 1443 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) |
3 | 2 | nfi 1442 | 1 ⊢ Ⅎ𝑥𝜑 |
Colors of variables: wff set class |
Syntax hints: Ⅎwnf 1440 |
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-gen 1429 |
This theorem depends on definitions: df-bi 116 df-nf 1441 |
This theorem is referenced by: nftru 1446 nfequid 1682 sbt 1764 sbc2ie 3008 omsinds 4581 |
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