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Mirrors > Home > ILE Home > Th. List > fliftel1 | Unicode version |
Description: Elementhood in the relation . (Contributed by Mario Carneiro, 23-Dec-2016.) |
Ref | Expression |
---|---|
flift.1 | |
flift.2 | |
flift.3 |
Ref | Expression |
---|---|
fliftel1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | flift.2 | . . . . 5 | |
2 | flift.3 | . . . . 5 | |
3 | opexg 4191 | . . . . 5 | |
4 | 1, 2, 3 | syl2anc 409 | . . . 4 |
5 | eqid 2157 | . . . . . 6 | |
6 | 5 | elrnmpt1 4840 | . . . . 5 |
7 | 6 | adantll 468 | . . . 4 |
8 | 4, 7 | mpdan 418 | . . 3 |
9 | flift.1 | . . 3 | |
10 | 8, 9 | eleqtrrdi 2251 | . 2 |
11 | df-br 3968 | . 2 | |
12 | 10, 11 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1335 wcel 2128 cvv 2712 cop 3564 class class class wbr 3967 cmpt 4028 crn 4590 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4085 ax-pow 4138 ax-pr 4172 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-rex 2441 df-v 2714 df-sbc 2938 df-csb 3032 df-un 3106 df-in 3108 df-ss 3115 df-pw 3546 df-sn 3567 df-pr 3568 df-op 3570 df-br 3968 df-opab 4029 df-mpt 4030 df-cnv 4597 df-dm 4599 df-rn 4600 |
This theorem is referenced by: fliftfun 5749 qliftel1 6564 |
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