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Mirrors > Home > ILE Home > Th. List > genpdflem | Unicode version |
Description: Simplification of upper or lower cut expression. Lemma for genpdf 6606. (Contributed by Jim Kingdon, 30-Sep-2019.) |
Ref | Expression |
---|---|
genpdflem.r | |
genpdflem.s |
Ref | Expression |
---|---|
genpdflem |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | genpdflem.r | . . . . . . . . 9 | |
2 | 1 | ex 108 | . . . . . . . 8 |
3 | 2 | pm4.71rd 374 | . . . . . . 7 |
4 | 3 | anbi1d 438 | . . . . . 6 |
5 | 4 | exbidv 1706 | . . . . 5 |
6 | 3anass 889 | . . . . . . . . . 10 | |
7 | 6 | rexbii 2331 | . . . . . . . . 9 |
8 | r19.42v 2467 | . . . . . . . . 9 | |
9 | 7, 8 | bitri 173 | . . . . . . . 8 |
10 | 9 | rexbii 2331 | . . . . . . 7 |
11 | df-rex 2312 | . . . . . . 7 | |
12 | 10, 11 | bitri 173 | . . . . . 6 |
13 | anass 381 | . . . . . . 7 | |
14 | 13 | exbii 1496 | . . . . . 6 |
15 | 12, 14 | bitr4i 176 | . . . . 5 |
16 | 5, 15 | syl6rbbr 188 | . . . 4 |
17 | df-rex 2312 | . . . 4 | |
18 | 16, 17 | syl6bbr 187 | . . 3 |
19 | genpdflem.s | . . . . . . . . . 10 | |
20 | 19 | ex 108 | . . . . . . . . 9 |
21 | 20 | pm4.71rd 374 | . . . . . . . 8 |
22 | 21 | anbi1d 438 | . . . . . . 7 |
23 | 22 | exbidv 1706 | . . . . . 6 |
24 | df-rex 2312 | . . . . . . 7 | |
25 | anass 381 | . . . . . . . 8 | |
26 | 25 | exbii 1496 | . . . . . . 7 |
27 | 24, 26 | bitr4i 176 | . . . . . 6 |
28 | 23, 27 | syl6rbbr 188 | . . . . 5 |
29 | df-rex 2312 | . . . . 5 | |
30 | 28, 29 | syl6bbr 187 | . . . 4 |
31 | 30 | rexbidv 2327 | . . 3 |
32 | 18, 31 | bitrd 177 | . 2 |
33 | 32 | rabbidv 2549 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 w3a 885 wceq 1243 wex 1381 wcel 1393 wrex 2307 crab 2310 (class class class)co 5512 cnq 6378 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-11 1397 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-ral 2311 df-rex 2312 df-rab 2315 |
This theorem is referenced by: genpdf 6606 |
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