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Mirrors > Home > MPE Home > Th. List > dmoprabss | Structured version Unicode version |
Description: The domain of an operation class abstraction. (Contributed by NM, 24-Aug-1995.) |
Ref | Expression |
---|---|
dmoprabss |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dmoprab 6282 |
. 2
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2 | 19.42v 1936 |
. . . 4
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3 | 2 | opabbii 4465 |
. . 3
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4 | opabssxp 5020 |
. . 3
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5 | 3, 4 | eqsstri 3495 |
. 2
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6 | 1, 5 | eqsstri 3495 |
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 4522 ax-nul 4530 ax-pr 4640 |
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 2650 df-rab 2808 df-v 3080 df-dif 3440 df-un 3442 df-in 3444 df-ss 3451 df-nul 3747 df-if 3901 df-sn 3987 df-pr 3989 df-op 3993 df-br 4402 df-opab 4460 df-xp 4955 df-dm 4959 df-oprab 6205 |
This theorem is referenced by: elmpt2cl 6415 oprabexd 6675 oprabex 6676 bropopvvv 6764 mpt2ndm0 6850 dmaddsr 9364 dmmulsr 9365 axaddf 9424 axmulf 9425 2wlkonot3v 30543 2spthonot3v 30544 |
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