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Mirrors > Home > MPE Home > Th. List > opelresg | Structured version Unicode version |
Description: Ordered pair membership in a restriction. Exercise 13 of [TakeutiZaring] p. 25. (Contributed by NM, 14-Oct-2005.) |
Ref | Expression |
---|---|
opelresg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opeq2 4163 |
. . 3
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2 | 1 | eleq1d 2521 |
. 2
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3 | 1 | eleq1d 2521 |
. . 3
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4 | 3 | anbi1d 704 |
. 2
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5 | vex 3075 |
. . 3
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6 | 5 | opelres 5219 |
. 2
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7 | 2, 4, 6 | vtoclbg 3131 |
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 1954 ax-ext 2431 ax-sep 4516 ax-nul 4524 ax-pr 4634 |
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-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2602 df-ne 2647 df-ral 2801 df-rex 2802 df-rab 2805 df-v 3074 df-dif 3434 df-un 3436 df-in 3438 df-ss 3445 df-nul 3741 df-if 3895 df-sn 3981 df-pr 3983 df-op 3987 df-opab 4454 df-xp 4949 df-res 4955 |
This theorem is referenced by: brresg 5222 opelresi 5225 issref 5314 |
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