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Mirrors > Home > ILE Home > Th. List > nfixpxy | Unicode version |
Description: Bound-variable hypothesis builder for indexed Cartesian product. (Contributed by Mario Carneiro, 15-Oct-2016.) (Revised by Jim Kingdon, 15-Feb-2023.) |
Ref | Expression |
---|---|
nfixp.1 |
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nfixp.2 |
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Ref | Expression |
---|---|
nfixpxy |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ixp 6523 |
. 2
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2 | nfcv 2240 |
. . . . 5
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3 | nftru 1410 |
. . . . . . 7
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4 | nfcvd 2241 |
. . . . . . . 8
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5 | nfixp.1 |
. . . . . . . . 9
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6 | 5 | a1i 9 |
. . . . . . . 8
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7 | 4, 6 | nfeld 2256 |
. . . . . . 7
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8 | 3, 7 | nfabd 2259 |
. . . . . 6
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9 | 8 | mptru 1308 |
. . . . 5
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10 | 2, 9 | nffn 5155 |
. . . 4
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11 | df-ral 2380 |
. . . . 5
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12 | 2 | a1i 9 |
. . . . . . . . . 10
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13 | 12, 4 | nffvd 5365 |
. . . . . . . . 9
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14 | nfixp.2 |
. . . . . . . . . 10
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15 | 14 | a1i 9 |
. . . . . . . . 9
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16 | 13, 15 | nfeld 2256 |
. . . . . . . 8
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17 | 7, 16 | nfimd 1532 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
18 | 3, 17 | nfald 1701 |
. . . . . 6
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19 | 18 | mptru 1308 |
. . . . 5
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20 | 11, 19 | nfxfr 1418 |
. . . 4
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21 | 10, 20 | nfan 1512 |
. . 3
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22 | 21 | nfab 2245 |
. 2
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23 | 1, 22 | nfcxfr 2237 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 |
This theorem depends on definitions: df-bi 116 df-3an 932 df-tru 1302 df-nf 1405 df-sb 1704 df-clab 2087 df-cleq 2093 df-clel 2096 df-nfc 2229 df-ral 2380 df-rex 2381 df-v 2643 df-un 3025 df-in 3027 df-ss 3034 df-sn 3480 df-pr 3481 df-op 3483 df-uni 3684 df-br 3876 df-opab 3930 df-rel 4484 df-cnv 4485 df-co 4486 df-dm 4487 df-iota 5024 df-fun 5061 df-fn 5062 df-fv 5067 df-ixp 6523 |
This theorem is referenced by: (None) |
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