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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 2671 |
. 2
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2 | elisset 2671 |
. 2
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3 | eeanv 1882 |
. . 3
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4 | nfe1 1455 |
. . . . 5
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5 | nfv 1491 |
. . . . 5
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6 | 4, 5 | nfbi 1551 |
. . . 4
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7 | nfe1 1455 |
. . . . . . 7
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8 | 7 | nfex 1599 |
. . . . . 6
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9 | nfv 1491 |
. . . . . 6
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10 | 8, 9 | nfbi 1551 |
. . . . 5
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11 | opeq12 3673 |
. . . . . . 7
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12 | copsexg 4126 |
. . . . . . . 8
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13 | 12 | eqcoms 2118 |
. . . . . . 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 189 |
. . . . 5
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17 | 10, 16 | exlimi 1556 |
. . . 4
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18 | 6, 17 | exlimi 1556 |
. . 3
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19 | 3, 18 | sylbir 134 |
. 2
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20 | 1, 2, 19 | syl2an 285 |
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 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-14 1475 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 ax-sep 4006 ax-pow 4058 ax-pr 4091 |
This theorem depends on definitions: df-bi 116 df-3an 947 df-tru 1317 df-nf 1420 df-sb 1719 df-eu 1978 df-mo 1979 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-v 2659 df-un 3041 df-in 3043 df-ss 3050 df-pw 3478 df-sn 3499 df-pr 3500 df-op 3502 |
This theorem is referenced by: opelopabga 4145 ov6g 5862 ltresr 7574 |
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