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Mirrors > Home > ILE Home > Th. List > dfse2 | Unicode version |
Description: Alternate definition of set-like relation. (Contributed by Mario Carneiro, 23-Jun-2015.) |
Ref | Expression |
---|---|
dfse2 | Se |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-se 4305 | . 2 Se | |
2 | dfrab3 3393 | . . . . 5 | |
3 | vex 2724 | . . . . . . 7 | |
4 | iniseg 4970 | . . . . . . 7 | |
5 | 3, 4 | ax-mp 5 | . . . . . 6 |
6 | 5 | ineq2i 3315 | . . . . 5 |
7 | 2, 6 | eqtr4i 2188 | . . . 4 |
8 | 7 | eleq1i 2230 | . . 3 |
9 | 8 | ralbii 2470 | . 2 |
10 | 1, 9 | bitri 183 | 1 Se |
Colors of variables: wff set class |
Syntax hints: wb 104 wceq 1342 wcel 2135 cab 2150 wral 2442 crab 2446 cvv 2721 cin 3110 csn 3570 class class class wbr 3976 Se wse 4301 ccnv 4597 cima 4601 |
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-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-rab 2451 df-v 2723 df-sbc 2947 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-br 3977 df-opab 4038 df-se 4305 df-xp 4604 df-cnv 4606 df-dm 4608 df-rn 4609 df-res 4610 df-ima 4611 |
This theorem is referenced by: isoselem 5782 |
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