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Mirrors > Home > ILE Home > Th. List > ndmfvg | Unicode version |
Description: The value of a class outside its domain is the empty set. (Contributed by Jim Kingdon, 15-Jan-2019.) |
Ref | Expression |
---|---|
ndmfvg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | euex 2027 | . . . . 5 | |
2 | eldmg 4729 | . . . . 5 | |
3 | 1, 2 | syl5ibr 155 | . . . 4 |
4 | 3 | con3d 620 | . . 3 |
5 | tz6.12-2 5405 | . . 3 | |
6 | 4, 5 | syl6 33 | . 2 |
7 | 6 | imp 123 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wceq 1331 wex 1468 wcel 1480 weu 1997 cvv 2681 c0 3358 class class class wbr 3924 cdm 4534 cfv 5118 |
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-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
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 2000 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-dif 3068 df-un 3070 df-in 3072 df-ss 3079 df-nul 3359 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-dm 4544 df-iota 5083 df-fv 5126 |
This theorem is referenced by: ovprc 5799 sumnul 11186 |
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