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Mirrors > Home > MPE Home > Th. List > dfoprab4f | Structured version Visualization version Unicode version |
Description: Operation class abstraction expressed without existential quantifiers. (Unnecessary distinct variable restrictions were removed by David Abernethy, 19-Jun-2012.) (Contributed by NM, 20-Dec-2008.) (Revised by Mario Carneiro, 31-Aug-2015.) |
Ref | Expression |
---|---|
dfoprab4f.x | |
dfoprab4f.y | |
dfoprab4f.1 |
Ref | Expression |
---|---|
dfoprab4f |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1843 | . . . . 5 | |
2 | dfoprab4f.x | . . . . . 6 | |
3 | nfs1v 2437 | . . . . . 6 | |
4 | 2, 3 | nfbi 1833 | . . . . 5 |
5 | 1, 4 | nfim 1825 | . . . 4 |
6 | opeq1 4402 | . . . . . 6 | |
7 | 6 | eqeq2d 2632 | . . . . 5 |
8 | sbequ12 2111 | . . . . . 6 | |
9 | 8 | bibi2d 332 | . . . . 5 |
10 | 7, 9 | imbi12d 334 | . . . 4 |
11 | nfv 1843 | . . . . . 6 | |
12 | dfoprab4f.y | . . . . . . 7 | |
13 | nfs1v 2437 | . . . . . . 7 | |
14 | 12, 13 | nfbi 1833 | . . . . . 6 |
15 | 11, 14 | nfim 1825 | . . . . 5 |
16 | opeq2 4403 | . . . . . . 7 | |
17 | 16 | eqeq2d 2632 | . . . . . 6 |
18 | sbequ12 2111 | . . . . . . 7 | |
19 | 18 | bibi2d 332 | . . . . . 6 |
20 | 17, 19 | imbi12d 334 | . . . . 5 |
21 | dfoprab4f.1 | . . . . 5 | |
22 | 15, 20, 21 | chvar 2262 | . . . 4 |
23 | 5, 10, 22 | chvar 2262 | . . 3 |
24 | 23 | dfoprab4 7225 | . 2 |
25 | nfv 1843 | . . 3 | |
26 | nfv 1843 | . . 3 | |
27 | nfv 1843 | . . . 4 | |
28 | 27, 3 | nfan 1828 | . . 3 |
29 | nfv 1843 | . . . 4 | |
30 | 13 | nfsb 2440 | . . . 4 |
31 | 29, 30 | nfan 1828 | . . 3 |
32 | eleq1 2689 | . . . . 5 | |
33 | eleq1 2689 | . . . . 5 | |
34 | 32, 33 | bi2anan9 917 | . . . 4 |
35 | 18, 8 | sylan9bbr 737 | . . . 4 |
36 | 34, 35 | anbi12d 747 | . . 3 |
37 | 25, 26, 28, 31, 36 | cbvoprab12 6729 | . 2 |
38 | 24, 37 | eqtr4i 2647 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wnf 1708 wsb 1880 wcel 1990 cop 4183 copab 4712 cxp 5112 coprab 6651 |
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-8 1992 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-pow 4843 ax-pr 4906 ax-un 6949 |
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 df-oprab 6654 df-1st 7168 df-2nd 7169 |
This theorem is referenced by: (None) |
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