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Mirrors > Home > ILE Home > Th. List > mapprc | Unicode version |
Description: When is a proper class, the class of all functions mapping to is empty. Exercise 4.41 of [Mendelson] p. 255. (Contributed by NM, 8-Dec-2003.) |
Ref | Expression |
---|---|
mapprc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | abn0m 3388 | . . . 4 | |
2 | fdm 5278 | . . . . . 6 | |
3 | vex 2689 | . . . . . . 7 | |
4 | 3 | dmex 4805 | . . . . . 6 |
5 | 2, 4 | eqeltrrdi 2231 | . . . . 5 |
6 | 5 | exlimiv 1577 | . . . 4 |
7 | 1, 6 | sylbi 120 | . . 3 |
8 | 7 | con3i 621 | . 2 |
9 | notm0 3383 | . 2 | |
10 | 8, 9 | sylib 121 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wceq 1331 wex 1468 wcel 1480 cab 2125 cvv 2686 c0 3363 cdm 4539 wf 5119 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 ax-un 4355 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-rex 2422 df-v 2688 df-dif 3073 df-un 3075 df-in 3077 df-ss 3084 df-nul 3364 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-opab 3990 df-cnv 4547 df-dm 4549 df-rn 4550 df-fn 5126 df-f 5127 |
This theorem is referenced by: (None) |
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