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Mirrors > Home > NFE Home > Th. List > dfiota4 | Unicode version |
Description: Alternate definition of iota in terms of 1c. (Contributed by SF, 29-Jan-2015.) |
Ref | Expression |
---|---|
dfiota4 | 1c |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iotauni 4351 | . . 3 | |
2 | dfeu2 4333 | . . . . . . . 8 1c | |
3 | snssi 3852 | . . . . . . . 8 1c 1c | |
4 | 2, 3 | sylbi 187 | . . . . . . 7 1c |
5 | df-ss 3259 | . . . . . . . 8 1c 1c | |
6 | incom 3448 | . . . . . . . . 9 1c 1c | |
7 | 6 | eqeq1i 2360 | . . . . . . . 8 1c 1c |
8 | 5, 7 | bitri 240 | . . . . . . 7 1c 1c |
9 | 4, 8 | sylib 188 | . . . . . 6 1c |
10 | 9 | unieqd 3902 | . . . . 5 1c |
11 | euabex 4334 | . . . . . 6 | |
12 | unisng 3908 | . . . . . 6 | |
13 | 11, 12 | syl 15 | . . . . 5 |
14 | 10, 13 | eqtrd 2385 | . . . 4 1c |
15 | 14 | unieqd 3902 | . . 3 1c |
16 | 1, 15 | eqtr4d 2388 | . 2 1c |
17 | iotanul 4354 | . . 3 | |
18 | 2 | notbii 287 | . . . . . . . 8 1c |
19 | disjsn 3786 | . . . . . . . 8 1c 1c | |
20 | 18, 19 | bitr4i 243 | . . . . . . 7 1c |
21 | 20 | biimpi 186 | . . . . . 6 1c |
22 | 21 | unieqd 3902 | . . . . 5 1c |
23 | 22 | unieqd 3902 | . . . 4 1c |
24 | uni0 3918 | . . . . . 6 | |
25 | 24 | unieqi 3901 | . . . . 5 |
26 | 25, 24 | eqtri 2373 | . . . 4 |
27 | 23, 26 | syl6eq 2401 | . . 3 1c |
28 | 17, 27 | eqtr4d 2388 | . 2 1c |
29 | 16, 28 | pm2.61i 156 | 1 1c |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wceq 1642 wcel 1710 weu 2204 cab 2339 cvv 2859 cin 3208 wss 3257 c0 3550 csn 3737 cuni 3891 1cc1c 4134 cio 4337 |
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-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 ax-nin 4078 ax-sn 4087 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-eu 2208 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ne 2518 df-ral 2619 df-rex 2620 df-v 2861 df-sbc 3047 df-nin 3211 df-compl 3212 df-in 3213 df-un 3214 df-dif 3215 df-ss 3259 df-nul 3551 df-sn 3741 df-pr 3742 df-uni 3892 df-1c 4136 df-iota 4339 |
This theorem is referenced by: (None) |
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