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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 1349 | . 2 ⊢ (φ → ∀xφ) |
3 | 2 | nfi 1348 | 1 ⊢ Ⅎxφ |
Colors of variables: wff set class |
Syntax hints: Ⅎwnf 1346 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-gen 1335 |
This theorem depends on definitions: df-bi 110 df-nf 1347 |
This theorem is referenced by: nftru 1352 nfequid 1587 sbt 1664 sbc2ie 2823 |
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