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Mirrors > Home > ILE Home > Th. List > fliftval | Unicode version |
Description: The value of the function . (Contributed by Mario Carneiro, 23-Dec-2016.) |
Ref | Expression |
---|---|
flift.1 | |
flift.2 | |
flift.3 | |
fliftval.4 | |
fliftval.5 | |
fliftval.6 |
Ref | Expression |
---|---|
fliftval |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fliftval.6 | . . 3 | |
2 | 1 | adantr 274 | . 2 |
3 | simpr 109 | . . . 4 | |
4 | eqidd 2140 | . . . . 5 | |
5 | eqidd 2140 | . . . . 5 | |
6 | 4, 5 | anim12ci 337 | . . . 4 |
7 | fliftval.4 | . . . . . . 7 | |
8 | 7 | eqeq2d 2151 | . . . . . 6 |
9 | fliftval.5 | . . . . . . 7 | |
10 | 9 | eqeq2d 2151 | . . . . . 6 |
11 | 8, 10 | anbi12d 464 | . . . . 5 |
12 | 11 | rspcev 2789 | . . . 4 |
13 | 3, 6, 12 | syl2anc 408 | . . 3 |
14 | flift.1 | . . . . 5 | |
15 | flift.2 | . . . . 5 | |
16 | flift.3 | . . . . 5 | |
17 | 14, 15, 16 | fliftel 5694 | . . . 4 |
18 | 17 | adantr 274 | . . 3 |
19 | 13, 18 | mpbird 166 | . 2 |
20 | funbrfv 5460 | . 2 | |
21 | 2, 19, 20 | sylc 62 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wcel 1480 wrex 2417 cop 3530 class class class wbr 3929 cmpt 3989 crn 4540 wfun 5117 cfv 5123 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-sbc 2910 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-opab 3990 df-mpt 3991 df-id 4215 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-rn 4550 df-iota 5088 df-fun 5125 df-fv 5131 |
This theorem is referenced by: qliftval 6515 |
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