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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ixp 6729 |
. 2
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2 | nfcv 2332 |
. . . . 5
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3 | nfab1 2334 |
. . . . 5
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4 | 2, 3 | nffn 5334 |
. . . 4
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5 | nfra1 2521 |
. . . 4
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6 | 4, 5 | nfan 1576 |
. . 3
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7 | 6 | nfab 2337 |
. 2
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8 | 1, 7 | nfcxfr 2329 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-sn 3616 df-pr 3617 df-op 3619 df-br 4022 df-opab 4083 df-rel 4654 df-cnv 4655 df-co 4656 df-dm 4657 df-fun 5240 df-fn 5241 df-ixp 6729 |
This theorem is referenced by: (None) |
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