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Mirrors > Home > ILE Home > Th. List > nfixp1 | Unicode version |
Description: The index variable in an indexed Cartesian product is not free. (Contributed by Jeff Madsen, 19-Jun-2011.) (Revised by Mario Carneiro, 15-Oct-2016.) |
Ref | Expression |
---|---|
nfixp1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ixp 6675 | . 2 | |
2 | nfcv 2312 | . . . . 5 | |
3 | nfab1 2314 | . . . . 5 | |
4 | 2, 3 | nffn 5292 | . . . 4 |
5 | nfra1 2501 | . . . 4 | |
6 | 4, 5 | nfan 1558 | . . 3 |
7 | 6 | nfab 2317 | . 2 |
8 | 1, 7 | nfcxfr 2309 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wcel 2141 cab 2156 wnfc 2299 wral 2448 wfn 5191 cfv 5196 cixp 6674 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-sn 3587 df-pr 3588 df-op 3590 df-br 3988 df-opab 4049 df-rel 4616 df-cnv 4617 df-co 4618 df-dm 4619 df-fun 5198 df-fn 5199 df-ixp 6675 |
This theorem is referenced by: (None) |
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