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Mirrors > Home > MPE Home > Th. List > rescnvcnv | Structured version Visualization version 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 5308 |
. . 3
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2 | 1 | reseq1i 5120 |
. 2
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3 | resres 5136 |
. 2
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4 | ssv 3464 |
. . . 4
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5 | sseqin2 3663 |
. . . 4
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6 | 4, 5 | mpbi 213 |
. . 3
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7 | 6 | reseq2i 5121 |
. 2
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8 | 2, 3, 7 | 3eqtri 2488 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-9 1907 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 ax-sep 4539 ax-nul 4548 ax-pr 4653 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 993 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-eu 2314 df-mo 2315 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-ne 2635 df-ral 2754 df-rex 2755 df-rab 2758 df-v 3059 df-dif 3419 df-un 3421 df-in 3423 df-ss 3430 df-nul 3744 df-if 3894 df-sn 3981 df-pr 3983 df-op 3987 df-br 4417 df-opab 4476 df-xp 4859 df-rel 4860 df-cnv 4861 df-res 4865 |
This theorem is referenced by: cnvcnvres 5318 imacnvcnv 5319 resdm2 5344 resdmres 5345 coires1 5372 f1oresrab 6079 |
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