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Mirrors > Home > MPE Home > Th. List > rescnvcnv | Structured 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 5392 |
. . 3
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2 | 1 | reseq1i 5207 |
. 2
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3 | resres 5224 |
. 2
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4 | ssv 3477 |
. . . 4
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5 | sseqin2 3670 |
. . . 4
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6 | 4, 5 | mpbi 208 |
. . 3
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7 | 6 | reseq2i 5208 |
. 2
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8 | 2, 3, 7 | 3eqtri 2484 |
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 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-9 1762 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1952 ax-ext 2430 ax-sep 4514 ax-nul 4522 ax-pr 4632 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-eu 2264 df-mo 2265 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2601 df-ne 2646 df-ral 2800 df-rex 2801 df-rab 2804 df-v 3073 df-dif 3432 df-un 3434 df-in 3436 df-ss 3443 df-nul 3739 df-if 3893 df-sn 3979 df-pr 3981 df-op 3985 df-br 4394 df-opab 4452 df-xp 4947 df-rel 4948 df-cnv 4949 df-res 4953 |
This theorem is referenced by: cnvcnvres 5403 imacnvcnv 5404 resdm2 5429 resdmres 5430 coires1 5456 f1oresrab 5977 |
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