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Mirrors > Home > NFE Home > Th. List > imacok | Unicode version |
Description: Image under a composition. (Contributed by SF, 4-Feb-2015.) |
Ref | Expression |
---|---|
imacok | k k kk |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2862 | . . . . . 6 | |
2 | vex 2862 | . . . . . 6 | |
3 | 1, 2 | opkelcok 4262 | . . . . 5 k |
4 | 3 | rexbii 2639 | . . . 4 k |
5 | rexcom4 2878 | . . . 4 | |
6 | df-rex 2620 | . . . . 5 k k | |
7 | vex 2862 | . . . . . . . . 9 | |
8 | 7 | elimak 4259 | . . . . . . . 8 k |
9 | 8 | anbi1i 676 | . . . . . . 7 k |
10 | r19.41v 2764 | . . . . . . 7 | |
11 | 9, 10 | bitr4i 243 | . . . . . 6 k |
12 | 11 | exbii 1582 | . . . . 5 k |
13 | 6, 12 | bitr2i 241 | . . . 4 k |
14 | 4, 5, 13 | 3bitri 262 | . . 3 k k |
15 | 2 | elimak 4259 | . . 3 k k k |
16 | 2 | elimak 4259 | . . 3 kk k |
17 | 14, 15, 16 | 3bitr4i 268 | . 2 k k kk |
18 | 17 | eqriv 2350 | 1 k k kk |
Colors of variables: wff setvar class |
Syntax hints: wa 358 wex 1541 wceq 1642 wcel 1710 wrex 2615 copk 4057 kcimak 4179 k ccomk 4180 |
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-3an 936 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ne 2518 df-rex 2620 df-v 2861 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-opk 4058 df-cnvk 4186 df-ins2k 4187 df-ins3k 4188 df-imak 4189 df-cok 4190 |
This theorem is referenced by: (None) |
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