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Mirrors > Home > MPE Home > Th. List > mpt2ndm0 | Structured version Unicode version |
Description: The value of an operation given by a maps-to rule is the empty set if the arguments are not contained in the base sets of the rule. (Contributed by Alexander van der Vekens, 12-Oct-2017.) |
Ref | Expression |
---|---|
mpt2ndm0.f |
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Ref | Expression |
---|---|
mpt2ndm0 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpt2ndm0.f |
. . . . 5
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2 | df-mpt2 6204 |
. . . . 5
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3 | 1, 2 | eqtri 2483 |
. . . 4
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4 | 3 | dmeqi 5148 |
. . 3
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5 | dmoprabss 6281 |
. . 3
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6 | 4, 5 | eqsstri 3493 |
. 2
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7 | nssdmovg 6354 |
. 2
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8 | 6, 7 | mpan 670 |
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-8 1760 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-pow 4577 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-ral 2803 df-rex 2804 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-uni 4199 df-br 4400 df-opab 4458 df-xp 4953 df-dm 4957 df-iota 5488 df-fv 5533 df-ov 6202 df-oprab 6203 df-mpt2 6204 |
This theorem is referenced by: brovex 6849 fullfunc 14934 fthfunc 14935 natfval 14974 evlval 17733 matbas0 18411 matrcl 18436 marrepfval 18497 marepvfval 18502 minmar1fval 18583 hmeofval 19462 nghmfval 20432 uvtxisvtx 23549 uvtx0 23550 uvtx01vtx 23551 elovmpt3imp 30307 2wlkonot3v 30541 2spthonot3v 30542 |
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