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Mirrors > Home > ILE Home > Th. List > elpmg | Unicode version |
Description: The predicate "is a partial function". (Contributed by Mario Carneiro, 14-Nov-2013.) |
Ref | Expression |
---|---|
elpmg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pmvalg 6652 |
. . . . 5
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2 | 1 | eleq2d 2247 |
. . . 4
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3 | funeq 5231 |
. . . . 5
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4 | 3 | elrab 2893 |
. . . 4
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5 | 2, 4 | bitrdi 196 |
. . 3
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6 | ancom 266 |
. . 3
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7 | 5, 6 | bitrdi 196 |
. 2
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8 | elex 2748 |
. . . . 5
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9 | 8 | a1i 9 |
. . . 4
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10 | xpexg 4736 |
. . . . . 6
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11 | 10 | ancoms 268 |
. . . . 5
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12 | ssexg 4139 |
. . . . . 6
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13 | 12 | expcom 116 |
. . . . 5
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14 | 11, 13 | syl 14 |
. . . 4
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15 | elpwg 3582 |
. . . . 5
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16 | 15 | a1i 9 |
. . . 4
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17 | 9, 14, 16 | pm5.21ndd 705 |
. . 3
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18 | 17 | anbi2d 464 |
. 2
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19 | 7, 18 | bitrd 188 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4118 ax-pow 4171 ax-pr 4205 ax-un 4429 ax-setind 4532 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-ral 2460 df-rex 2461 df-rab 2464 df-v 2739 df-sbc 2963 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-pw 3576 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-br 4001 df-opab 4062 df-id 4289 df-xp 4628 df-rel 4629 df-cnv 4630 df-co 4631 df-dm 4632 df-iota 5173 df-fun 5213 df-fv 5219 df-ov 5871 df-oprab 5872 df-mpo 5873 df-pm 6644 |
This theorem is referenced by: elpm2g 6658 pmss12g 6668 elpm 6672 pmsspw 6676 ennnfonelemj0 12372 lmfss 13377 |
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