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Mirrors > Home > ILE Home > Th. List > tposexg | Unicode version |
Description: The transposition of a set is a set. (Contributed by Mario Carneiro, 10-Sep-2015.) |
Ref | Expression |
---|---|
tposexg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tposssxp 6249 |
. 2
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2 | dmexg 4891 |
. . . . 5
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3 | cnvexg 5166 |
. . . . 5
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4 | 2, 3 | syl 14 |
. . . 4
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5 | p0ex 4188 |
. . . 4
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6 | unexg 4443 |
. . . 4
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7 | 4, 5, 6 | sylancl 413 |
. . 3
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8 | rnexg 4892 |
. . 3
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9 | xpexg 4740 |
. . 3
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10 | 7, 8, 9 | syl2anc 411 |
. 2
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11 | ssexg 4142 |
. 2
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12 | 1, 10, 11 | sylancr 414 |
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-in1 614 ax-in2 615 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-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4121 ax-nul 4129 ax-pow 4174 ax-pr 4209 ax-un 4433 |
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-ral 2460 df-rex 2461 df-rab 2464 df-v 2739 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-nul 3423 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-br 4004 df-opab 4065 df-mpt 4066 df-xp 4632 df-rel 4633 df-cnv 4634 df-co 4635 df-dm 4636 df-rn 4637 df-res 4638 df-ima 4639 df-tpos 6245 |
This theorem is referenced by: tposex 6278 opprvalg 13194 opprmulfvalg 13195 opprex 13198 opprsllem 13199 |
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