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Mirrors > Home > NFE Home > Th. List > enprmaplem1 | Unicode version |
Description: Lemma for enprmap 6082. Set up stratification. (Contributed by SF, 3-Mar-2015.) |
Ref | Expression |
---|---|
enprmaplem1.1 |
Ref | Expression |
---|---|
enprmaplem1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | enprmaplem1.1 | . . 3 | |
2 | elima1c 4947 | . . . . . . 7 SI S 1c SI S | |
3 | oteltxp 5782 | . . . . . . . . 9 SI S SI S | |
4 | vex 2862 | . . . . . . . . . . . 12 | |
5 | vex 2862 | . . . . . . . . . . . 12 | |
6 | 4, 5 | opsnelsi 5774 | . . . . . . . . . . 11 SI |
7 | df-br 4640 | . . . . . . . . . . . 12 | |
8 | brres 4949 | . . . . . . . . . . . . 13 | |
9 | eliniseg 5020 | . . . . . . . . . . . . . 14 | |
10 | 9 | anbi2i 675 | . . . . . . . . . . . . 13 |
11 | 8, 10 | bitri 240 | . . . . . . . . . . . 12 |
12 | 7, 11 | bitr3i 242 | . . . . . . . . . . 11 |
13 | vex 2862 | . . . . . . . . . . . 12 | |
14 | 5, 13 | op1st2nd 5790 | . . . . . . . . . . 11 |
15 | 6, 12, 14 | 3bitri 262 | . . . . . . . . . 10 SI |
16 | vex 2862 | . . . . . . . . . . 11 | |
17 | 4, 16 | opelssetsn 4760 | . . . . . . . . . 10 S |
18 | 15, 17 | anbi12i 678 | . . . . . . . . 9 SI S |
19 | 3, 18 | bitri 240 | . . . . . . . 8 SI S |
20 | 19 | exbii 1582 | . . . . . . 7 SI S |
21 | 2, 20 | bitri 240 | . . . . . 6 SI S 1c |
22 | 5, 13 | opex 4588 | . . . . . . . 8 |
23 | eleq1 2413 | . . . . . . . 8 | |
24 | 22, 23 | ceqsexv 2894 | . . . . . . 7 |
25 | df-br 4640 | . . . . . . 7 | |
26 | 24, 25 | bitr4i 243 | . . . . . 6 |
27 | 21, 26 | bitri 240 | . . . . 5 SI S 1c |
28 | eliniseg 5020 | . . . . 5 | |
29 | 27, 28 | bitr4i 243 | . . . 4 SI S 1c |
30 | 29 | releqmpt 5808 | . . 3 ∼ Ins3 S Ins2 SI S 1c1c |
31 | 1, 30 | eqtr4i 2376 | . 2 ∼ Ins3 S Ins2 SI S 1c1c |
32 | ovex 5551 | . . 3 | |
33 | 1stex 4739 | . . . . . . 7 | |
34 | 2ndex 5112 | . . . . . . . . 9 | |
35 | 34 | cnvex 5102 | . . . . . . . 8 |
36 | snex 4111 | . . . . . . . 8 | |
37 | 35, 36 | imaex 4747 | . . . . . . 7 |
38 | 33, 37 | resex 5117 | . . . . . 6 |
39 | 38 | siex 4753 | . . . . 5 SI |
40 | ssetex 4744 | . . . . 5 S | |
41 | 39, 40 | txpex 5785 | . . . 4 SI S |
42 | 1cex 4142 | . . . 4 1c | |
43 | 41, 42 | imaex 4747 | . . 3 SI S 1c |
44 | 32, 43 | mptexlem 5810 | . 2 ∼ Ins3 S Ins2 SI S 1c1c |
45 | 31, 44 | eqeltri 2423 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wa 358 wex 1541 wceq 1642 wcel 1710 cvv 2859 ∼ ccompl 3205 cin 3208 csymdif 3209 csn 3737 1cc1c 4134 cop 4561 class class class wbr 4639 c1st 4717 S csset 4719 SI csi 4720 cima 4722 cxp 4770 ccnv 4771 cres 4774 c2nd 4783 (class class class)co 5525 cmpt 5651 ctxp 5735 Ins2 cins2 5749 Ins3 cins3 5751 cmap 5999 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-13 1712 ax-14 1714 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 ax-nin 4078 ax-xp 4079 ax-cnv 4080 ax-1c 4081 ax-sset 4082 ax-si 4083 ax-ins2 4084 ax-ins3 4085 ax-typlower 4086 ax-sn 4087 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-3or 935 df-3an 936 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-eu 2208 df-mo 2209 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ne 2518 df-ral 2619 df-rex 2620 df-reu 2621 df-rmo 2622 df-rab 2623 df-v 2861 df-sbc 3047 df-nin 3211 df-compl 3212 df-in 3213 df-un 3214 df-dif 3215 df-symdif 3216 df-ss 3259 df-pss 3261 df-nul 3551 df-if 3663 df-pw 3724 df-sn 3741 df-pr 3742 df-uni 3892 df-int 3927 df-opk 4058 df-1c 4136 df-pw1 4137 df-uni1 4138 df-xpk 4185 df-cnvk 4186 df-ins2k 4187 df-ins3k 4188 df-imak 4189 df-cok 4190 df-p6 4191 df-sik 4192 df-ssetk 4193 df-imagek 4194 df-idk 4195 df-iota 4339 df-0c 4377 df-addc 4378 df-nnc 4379 df-fin 4380 df-lefin 4440 df-ltfin 4441 df-ncfin 4442 df-tfin 4443 df-evenfin 4444 df-oddfin 4445 df-sfin 4446 df-spfin 4447 df-phi 4565 df-op 4566 df-proj1 4567 df-proj2 4568 df-opab 4623 df-br 4640 df-1st 4723 df-swap 4724 df-sset 4725 df-co 4726 df-ima 4727 df-si 4728 df-xp 4784 df-cnv 4785 df-rn 4786 df-dm 4787 df-res 4788 df-fv 4795 df-2nd 4797 df-ov 5526 df-mpt 5652 df-txp 5736 df-ins2 5750 df-ins3 5752 |
This theorem is referenced by: enprmap 6082 |
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