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Mirrors > Home > ILE Home > Th. List > copsex2g | Unicode version |
Description: Implicit substitution inference for ordered pairs. (Contributed by NM, 28-May-1995.) |
Ref | Expression |
---|---|
copsex2g.1 |
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Ref | Expression |
---|---|
copsex2g |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elisset 2751 |
. 2
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2 | elisset 2751 |
. 2
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3 | eeanv 1932 |
. . 3
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4 | nfe1 1496 |
. . . . 5
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5 | nfv 1528 |
. . . . 5
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6 | 4, 5 | nfbi 1589 |
. . . 4
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7 | nfe1 1496 |
. . . . . . 7
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8 | 7 | nfex 1637 |
. . . . . 6
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9 | nfv 1528 |
. . . . . 6
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10 | 8, 9 | nfbi 1589 |
. . . . 5
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11 | opeq12 3778 |
. . . . . . 7
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12 | copsexg 4240 |
. . . . . . . 8
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13 | 12 | eqcoms 2180 |
. . . . . . 7
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14 | 11, 13 | syl 14 |
. . . . . 6
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15 | copsex2g.1 |
. . . . . 6
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16 | 14, 15 | bitr3d 190 |
. . . . 5
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17 | 10, 16 | exlimi 1594 |
. . . 4
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18 | 6, 17 | exlimi 1594 |
. . 3
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19 | 3, 18 | sylbir 135 |
. 2
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20 | 1, 2, 19 | syl2an 289 |
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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4118 ax-pow 4171 ax-pr 4205 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-pw 3576 df-sn 3597 df-pr 3598 df-op 3600 |
This theorem is referenced by: opelopabga 4259 ov6g 6005 ltresr 7816 |
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