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Mirrors > Home > ILE Home > Th. List > rescnvcnv | Unicode version |
Description: The restriction of the double converse of a class. (Contributed by NM, 8-Apr-2007.) (Proof shortened by Andrew Salmon, 27-Aug-2011.) |
Ref | Expression |
---|---|
rescnvcnv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnvcnv2 5083 |
. . 3
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2 | 1 | reseq1i 4904 |
. 2
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3 | resres 4920 |
. 2
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4 | ssv 3178 |
. . . 4
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5 | sseqin2 3355 |
. . . 4
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6 | 4, 5 | mpbi 145 |
. . 3
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7 | 6 | reseq2i 4905 |
. 2
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8 | 2, 3, 7 | 3eqtri 2202 |
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 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-14 2151 ax-ext 2159 ax-sep 4122 ax-pow 4175 ax-pr 4210 |
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-v 2740 df-un 3134 df-in 3136 df-ss 3143 df-pw 3578 df-sn 3599 df-pr 3600 df-op 3602 df-br 4005 df-opab 4066 df-xp 4633 df-rel 4634 df-cnv 4635 df-res 4639 |
This theorem is referenced by: cnvcnvres 5093 imacnvcnv 5094 resdm2 5120 resdmres 5121 coires1 5147 cocnvres 5154 f1oresrab 5682 |
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