Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > elrabi | Unicode version |
Description: Implication for the membership in a restricted class abstraction. (Contributed by Alexander van der Vekens, 31-Dec-2017.) |
Ref | Expression |
---|---|
elrabi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | clelab 2290 | . . 3 | |
2 | eleq1 2227 | . . . . . 6 | |
3 | 2 | anbi1d 461 | . . . . 5 |
4 | 3 | simprbda 381 | . . . 4 |
5 | 4 | exlimiv 1585 | . . 3 |
6 | 1, 5 | sylbi 120 | . 2 |
7 | df-rab 2451 | . 2 | |
8 | 6, 7 | eleq2s 2259 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1342 wex 1479 wcel 2135 cab 2150 crab 2446 |
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-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-11 1493 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-rab 2451 |
This theorem is referenced by: ordtriexmidlem 4490 ordtri2or2exmidlem 4497 onsucelsucexmidlem 4500 ordsoexmid 4533 reg3exmidlemwe 4550 elfvmptrab1 5574 acexmidlemcase 5831 ssfirab 6890 exmidonfinlem 7140 cc4f 7201 genpelvl 7444 genpelvu 7445 suplocsrlempr 7739 nnindnn 7825 sup3exmid 8843 nnind 8864 supinfneg 9524 infsupneg 9525 supminfex 9526 ublbneg 9542 hashinfuni 10679 zsupcllemstep 11863 infssuzex 11867 infssuzledc 11868 bezoutlemsup 11927 lcmgcdlem 11988 phisum 12151 oddennn 12268 evenennn 12269 znnen 12274 ennnfonelemg 12279 txdis1cn 12825 reopnap 13085 divcnap 13102 limccl 13175 dvlemap 13196 dvaddxxbr 13212 dvmulxxbr 13213 dvcoapbr 13218 dvcjbr 13219 dvrecap 13224 dveflem 13234 |
Copyright terms: Public domain | W3C validator |