Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > imadiflem | Unicode version |
Description: One direction of imadif 5276. This direction does not require . (Contributed by Jim Kingdon, 25-Dec-2018.) |
Ref | Expression |
---|---|
imadiflem |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2454 | . . . 4 | |
2 | df-rex 2454 | . . . . 5 | |
3 | 2 | notbii 663 | . . . 4 |
4 | alnex 1492 | . . . . . . 7 | |
5 | 19.29r 1614 | . . . . . . 7 | |
6 | 4, 5 | sylan2br 286 | . . . . . 6 |
7 | simpl 108 | . . . . . . . . 9 | |
8 | simplr 525 | . . . . . . . . . 10 | |
9 | simpr 109 | . . . . . . . . . . 11 | |
10 | ancom 264 | . . . . . . . . . . . . 13 | |
11 | 10 | notbii 663 | . . . . . . . . . . . 12 |
12 | imnan 685 | . . . . . . . . . . . 12 | |
13 | 11, 12 | bitr4i 186 | . . . . . . . . . . 11 |
14 | 9, 13 | sylib 121 | . . . . . . . . . 10 |
15 | 8, 14 | mpd 13 | . . . . . . . . 9 |
16 | 7, 15, 8 | jca32 308 | . . . . . . . 8 |
17 | eldif 3130 | . . . . . . . . . 10 | |
18 | 17 | anbi1i 455 | . . . . . . . . 9 |
19 | anandir 586 | . . . . . . . . 9 | |
20 | 18, 19 | bitri 183 | . . . . . . . 8 |
21 | 16, 20 | sylibr 133 | . . . . . . 7 |
22 | 21 | eximi 1593 | . . . . . 6 |
23 | 6, 22 | syl 14 | . . . . 5 |
24 | df-rex 2454 | . . . . 5 | |
25 | 23, 24 | sylibr 133 | . . . 4 |
26 | 1, 3, 25 | syl2anb 289 | . . 3 |
27 | 26 | ss2abi 3219 | . 2 |
28 | dfima2 4953 | . . . 4 | |
29 | dfima2 4953 | . . . 4 | |
30 | 28, 29 | difeq12i 3243 | . . 3 |
31 | difab 3396 | . . 3 | |
32 | 30, 31 | eqtri 2191 | . 2 |
33 | dfima2 4953 | . 2 | |
34 | 27, 32, 33 | 3sstr4i 3188 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wal 1346 wex 1485 wcel 2141 cab 2156 wrex 2449 cdif 3118 wss 3121 class class class wbr 3987 cima 4612 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4105 ax-pow 4158 ax-pr 4192 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-fal 1354 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-rab 2457 df-v 2732 df-dif 3123 df-un 3125 df-in 3127 df-ss 3134 df-pw 3566 df-sn 3587 df-pr 3588 df-op 3590 df-br 3988 df-opab 4049 df-xp 4615 df-cnv 4617 df-dm 4619 df-rn 4620 df-res 4621 df-ima 4622 |
This theorem is referenced by: imadif 5276 |
Copyright terms: Public domain | W3C validator |