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Mirrors > Home > ILE Home > Th. List > nfsuc | GIF version |
Description: Bound-variable hypothesis builder for successor. (Contributed by NM, 15-Sep-2003.) |
Ref | Expression |
---|---|
nfsuc.1 | ⊢ Ⅎ𝑥𝐴 |
Ref | Expression |
---|---|
nfsuc | ⊢ Ⅎ𝑥 suc 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-suc 4301 | . 2 ⊢ suc 𝐴 = (𝐴 ∪ {𝐴}) | |
2 | nfsuc.1 | . . 3 ⊢ Ⅎ𝑥𝐴 | |
3 | 2 | nfsn 3591 | . . 3 ⊢ Ⅎ𝑥{𝐴} |
4 | 2, 3 | nfun 3237 | . 2 ⊢ Ⅎ𝑥(𝐴 ∪ {𝐴}) |
5 | 1, 4 | nfcxfr 2279 | 1 ⊢ Ⅎ𝑥 suc 𝐴 |
Colors of variables: wff set class |
Syntax hints: Ⅎwnfc 2269 ∪ cun 3074 {csn 3532 suc csuc 4295 |
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-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-un 3080 df-sn 3538 df-pr 3539 df-suc 4301 |
This theorem is referenced by: (None) |
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