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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 2472 |
. 2
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2 | pm4.71 389 |
. . 3
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3 | 2 | albii 1480 |
. 2
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4 | dmopab 4852 |
. . . . 5
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5 | 19.42v 1917 |
. . . . . 6
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6 | 5 | abbii 2304 |
. . . . 5
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7 | 4, 6 | eqtri 2209 |
. . . 4
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8 | 7 | eqeq1i 2196 |
. . 3
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9 | eqcom 2190 |
. . 3
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10 | abeq2 2297 |
. . 3
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11 | 8, 9, 10 | 3bitr2ri 209 |
. 2
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12 | 1, 3, 11 | 3bitri 206 |
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 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-14 2162 ax-ext 2170 ax-sep 4135 ax-pow 4188 ax-pr 4223 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-nf 1471 df-sb 1773 df-eu 2040 df-mo 2041 df-clab 2175 df-cleq 2181 df-clel 2184 df-nfc 2320 df-ral 2472 df-v 2753 df-un 3147 df-in 3149 df-ss 3156 df-pw 3591 df-sn 3612 df-pr 3613 df-op 3615 df-br 4018 df-opab 4079 df-dm 4650 |
This theorem is referenced by: dmxpm 4861 dmxpid 4862 fnopabg 5353 acfun 7223 ccfunen 7280 |
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