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Mirrors > Home > MPE Home > Th. List > fliftval | Structured version Visualization version 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 481 | . 2 |
3 | simpr 477 | . . . 4 | |
4 | eqidd 2623 | . . . . 5 | |
5 | eqidd 2623 | . . . . 5 | |
6 | 4, 5 | anim12ci 591 | . . . 4 |
7 | fliftval.4 | . . . . . . 7 | |
8 | 7 | eqeq2d 2632 | . . . . . 6 |
9 | fliftval.5 | . . . . . . 7 | |
10 | 9 | eqeq2d 2632 | . . . . . 6 |
11 | 8, 10 | anbi12d 747 | . . . . 5 |
12 | 11 | rspcev 3309 | . . . 4 |
13 | 3, 6, 12 | syl2anc 693 | . . 3 |
14 | flift.1 | . . . . 5 | |
15 | flift.2 | . . . . 5 | |
16 | flift.3 | . . . . 5 | |
17 | 14, 15, 16 | fliftel 6559 | . . . 4 |
18 | 17 | adantr 481 | . . 3 |
19 | 13, 18 | mpbird 247 | . 2 |
20 | funbrfv 6234 | . 2 | |
21 | 2, 19, 20 | sylc 65 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wcel 1990 wrex 2913 cop 4183 class class class wbr 4653 cmpt 4729 crn 5115 wfun 5882 cfv 5888 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-iota 5851 df-fun 5890 df-fv 5896 |
This theorem is referenced by: qliftval 7836 cygznlem2 19917 pi1xfrval 22854 pi1coval 22860 |
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