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Mirrors > Home > ILE Home > Th. List > dmopab3 | Unicode version |
Description: The domain of a restricted class of ordered pairs. (Contributed by NM, 31-Jan-2004.) |
Ref | Expression |
---|---|
dmopab3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 2395 |
. 2
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2 | pm4.71 384 |
. . 3
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3 | 2 | albii 1429 |
. 2
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4 | dmopab 4710 |
. . . . 5
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5 | 19.42v 1860 |
. . . . . 6
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6 | 5 | abbii 2230 |
. . . . 5
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7 | 4, 6 | eqtri 2135 |
. . . 4
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8 | 7 | eqeq1i 2122 |
. . 3
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9 | eqcom 2117 |
. . 3
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10 | abeq2 2223 |
. . 3
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11 | 8, 9, 10 | 3bitr2ri 208 |
. 2
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12 | 1, 3, 11 | 3bitri 205 |
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-ral 2395 df-v 2659 df-un 3041 df-in 3043 df-ss 3050 df-pw 3478 df-sn 3499 df-pr 3500 df-op 3502 df-br 3896 df-opab 3950 df-dm 4509 |
This theorem is referenced by: dmxpm 4719 dmxpid 4720 fnopabg 5204 acfun 7011 ccfunen 7027 |
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