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Mirrors > Home > ILE Home > Th. List > qliftf | Unicode version |
Description: The domain and range of the function . (Contributed by Mario Carneiro, 23-Dec-2016.) |
Ref | Expression |
---|---|
qlift.1 | |
qlift.2 | |
qlift.3 | |
qlift.4 |
Ref | Expression |
---|---|
qliftf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | qlift.1 | . . 3 | |
2 | qlift.2 | . . . 4 | |
3 | qlift.3 | . . . 4 | |
4 | qlift.4 | . . . 4 | |
5 | 1, 2, 3, 4 | qliftlem 6555 | . . 3 |
6 | 1, 5, 2 | fliftf 5746 | . 2 |
7 | df-qs 6483 | . . . . 5 | |
8 | eqid 2157 | . . . . . 6 | |
9 | 8 | rnmpt 4833 | . . . . 5 |
10 | 7, 9 | eqtr4i 2181 | . . . 4 |
11 | 10 | a1i 9 | . . 3 |
12 | 11 | feq2d 5306 | . 2 |
13 | 6, 12 | bitr4d 190 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1335 wcel 2128 cab 2143 wrex 2436 cvv 2712 cop 3563 cmpt 4025 crn 4586 wfun 5163 wf 5165 wer 6474 cec 6475 cqs 6476 |
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-13 2130 ax-14 2131 ax-ext 2139 ax-sep 4082 ax-pow 4135 ax-pr 4169 ax-un 4393 |
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-ral 2440 df-rex 2441 df-rab 2444 df-v 2714 df-sbc 2938 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3773 df-br 3966 df-opab 4026 df-mpt 4027 df-id 4253 df-xp 4591 df-rel 4592 df-cnv 4593 df-co 4594 df-dm 4595 df-rn 4596 df-res 4597 df-ima 4598 df-iota 5134 df-fun 5171 df-fn 5172 df-f 5173 df-fv 5177 df-er 6477 df-ec 6479 df-qs 6483 |
This theorem is referenced by: (None) |
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