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Mirrors > Home > NFE Home > Th. List > abexv | Unicode version |
Description: When does not occur in , is a set. (Contributed by SF, 17-Jan-2015.) |
Ref | Expression |
---|---|
abexv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | abvor0 3567 | . 2 | |
2 | vvex 4109 | . . . 4 | |
3 | eleq1 2413 | . . . 4 | |
4 | 2, 3 | mpbiri 224 | . . 3 |
5 | 0ex 4110 | . . . 4 | |
6 | eleq1 2413 | . . . 4 | |
7 | 5, 6 | mpbiri 224 | . . 3 |
8 | 4, 7 | jaoi 368 | . 2 |
9 | 1, 8 | ax-mp 5 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wo 357 wceq 1642 wcel 1710 cab 2339 cvv 2859 c0 3550 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 ax-nin 4078 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-un 3214 df-dif 3215 df-ss 3259 df-nul 3551 |
This theorem is referenced by: nncaddccl 4419 preaddccan2lem1 4454 ltfintrilem1 4465 leconnnc 6218 addccan2nclem2 6264 nchoicelem16 6304 |
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