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Mirrors > Home > MPE Home > Th. List > ovprc | Structured version Visualization version Unicode version |
Description: The value of an operation when the one of the arguments is a proper class. Note: this theorem is dependent on our particular definitions of operation value, function value, and ordered pair. (Contributed by Mario Carneiro, 26-Apr-2015.) |
Ref | Expression |
---|---|
ovprc1.1 |
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Ref | Expression |
---|---|
ovprc |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ov 6311 |
. 2
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2 | df-br 4396 |
. . . . 5
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3 | ovprc1.1 |
. . . . . 6
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4 | brrelex12 4877 |
. . . . . 6
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5 | 3, 4 | mpan 684 |
. . . . 5
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6 | 2, 5 | sylbir 218 |
. . . 4
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7 | 6 | con3i 142 |
. . 3
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8 | ndmfv 5903 |
. . 3
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9 | 7, 8 | syl 17 |
. 2
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10 | 1, 9 | syl5eq 2517 |
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 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-8 1906 ax-9 1913 ax-10 1932 ax-11 1937 ax-12 1950 ax-13 2104 ax-ext 2451 ax-sep 4518 ax-nul 4527 ax-pow 4579 ax-pr 4639 |
This theorem depends on definitions: df-bi 190 df-or 377 df-an 378 df-3an 1009 df-tru 1455 df-ex 1672 df-nf 1676 df-sb 1806 df-eu 2323 df-mo 2324 df-clab 2458 df-cleq 2464 df-clel 2467 df-nfc 2601 df-ne 2643 df-ral 2761 df-rex 2762 df-rab 2765 df-v 3033 df-dif 3393 df-un 3395 df-in 3397 df-ss 3404 df-nul 3723 df-if 3873 df-sn 3960 df-pr 3962 df-op 3966 df-uni 4191 df-br 4396 df-opab 4455 df-xp 4845 df-rel 4846 df-dm 4849 df-iota 5553 df-fv 5597 df-ov 6311 |
This theorem is referenced by: ovprc1 6339 ovprc2 6340 ovrcl 6341 elbasov 15249 firest 15409 psrplusg 18682 psrmulr 18685 psrvscafval 18691 mplval 18729 opsrle 18776 opsrbaslem 18778 evlval 18824 matbas0pc 19511 mdetfval 19688 madufval 19739 mdegfval 23090 nbgrprc0 39566 |
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