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Mirrors > Home > MPE Home > Th. List > opelcnvg | Structured version Unicode version |
Description: Ordered-pair membership in converse. (Contributed by NM, 13-May-1999.) (Proof shortened by Andrew Salmon, 27-Aug-2011.) |
Ref | Expression |
---|---|
opelcnvg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq2 4403 |
. . 3
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2 | breq1 4402 |
. . 3
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3 | df-cnv 4955 |
. . 3
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4 | 1, 2, 3 | brabg 4715 |
. 2
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5 | df-br 4400 |
. 2
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6 | df-br 4400 |
. 2
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7 | 4, 5, 6 | 3bitr3g 287 |
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 1955 ax-ext 2432 ax-sep 4520 ax-nul 4528 ax-pr 4638 |
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 2266 df-mo 2267 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2604 df-ne 2649 df-rab 2807 df-v 3078 df-dif 3438 df-un 3440 df-in 3442 df-ss 3449 df-nul 3745 df-if 3899 df-sn 3985 df-pr 3987 df-op 3991 df-br 4400 df-opab 4458 df-cnv 4955 |
This theorem is referenced by: brcnvg 5127 opelcnv 5128 fvimacnv 5926 brtpos 6863 xrlenlt 9552 elpredim 27780 brcolinear2 28232 |
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