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Mirrors > Home > ILE Home > Th. List > nfnf1 | GIF version |
Description: 𝑥 is not free in Ⅎ𝑥𝜑. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
nfnf1 | ⊢ Ⅎ𝑥Ⅎ𝑥𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-nf 1350 | . 2 ⊢ (Ⅎ𝑥𝜑 ↔ ∀𝑥(𝜑 → ∀𝑥𝜑)) | |
2 | nfa1 1434 | . 2 ⊢ Ⅎ𝑥∀𝑥(𝜑 → ∀𝑥𝜑) | |
3 | 1, 2 | nfxfr 1363 | 1 ⊢ Ⅎ𝑥Ⅎ𝑥𝜑 |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∀wal 1241 Ⅎwnf 1349 |
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-5 1336 ax-gen 1338 ax-ial 1427 |
This theorem depends on definitions: df-bi 110 df-nf 1350 |
This theorem is referenced by: nfimd 1477 nfnt 1546 nfald 1643 equs5or 1711 sbcomxyyz 1846 nfsb4t 1890 nfnfc1 2181 sbcnestgf 2897 dfnfc2 3598 bdsepnft 10007 setindft 10090 strcollnft 10109 |
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