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Mirrors > Home > ILE Home > Th. List > unixpm | Unicode version |
Description: The double class union of an inhabited cross product is the union of its members. (Contributed by Jim Kingdon, 18-Dec-2018.) |
Ref | Expression |
---|---|
unixpm |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | relxp 4760 |
. . 3
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2 | relfld 5182 |
. . 3
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3 | 1, 2 | ax-mp 5 |
. 2
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4 | ancom 266 |
. . . 4
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5 | xpm 5075 |
. . . 4
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6 | 4, 5 | bitri 184 |
. . 3
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7 | dmxpm 4872 |
. . . 4
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8 | rnxpm 5083 |
. . . 4
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9 | uneq12 3304 |
. . . 4
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10 | 7, 8, 9 | syl2an 289 |
. . 3
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11 | 6, 10 | sylbir 135 |
. 2
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12 | 3, 11 | eqtrid 2234 |
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 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-14 2163 ax-ext 2171 ax-sep 4143 ax-pow 4199 ax-pr 4234 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2758 df-un 3153 df-in 3155 df-ss 3162 df-pw 3599 df-sn 3620 df-pr 3621 df-op 3623 df-uni 3832 df-br 4026 df-opab 4087 df-xp 4657 df-rel 4658 df-cnv 4659 df-dm 4661 df-rn 4662 |
This theorem is referenced by: (None) |
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