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Mirrors > Home > ILE Home > Th. List > genpdflem | Unicode version |
Description: Simplification of upper or lower cut expression. Lemma for genpdf 7316. (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 114 | . . . . . . . 8 |
3 | 2 | pm4.71rd 391 | . . . . . . 7 |
4 | 3 | anbi1d 460 | . . . . . 6 |
5 | 4 | exbidv 1797 | . . . . 5 |
6 | 3anass 966 | . . . . . . . . . 10 | |
7 | 6 | rexbii 2442 | . . . . . . . . 9 |
8 | r19.42v 2588 | . . . . . . . . 9 | |
9 | 7, 8 | bitri 183 | . . . . . . . 8 |
10 | 9 | rexbii 2442 | . . . . . . 7 |
11 | df-rex 2422 | . . . . . . 7 | |
12 | 10, 11 | bitri 183 | . . . . . 6 |
13 | anass 398 | . . . . . . 7 | |
14 | 13 | exbii 1584 | . . . . . 6 |
15 | 12, 14 | bitr4i 186 | . . . . 5 |
16 | 5, 15 | syl6rbbr 198 | . . . 4 |
17 | df-rex 2422 | . . . 4 | |
18 | 16, 17 | syl6bbr 197 | . . 3 |
19 | genpdflem.s | . . . . . . . . . 10 | |
20 | 19 | ex 114 | . . . . . . . . 9 |
21 | 20 | pm4.71rd 391 | . . . . . . . 8 |
22 | 21 | anbi1d 460 | . . . . . . 7 |
23 | 22 | exbidv 1797 | . . . . . 6 |
24 | df-rex 2422 | . . . . . . 7 | |
25 | anass 398 | . . . . . . . 8 | |
26 | 25 | exbii 1584 | . . . . . . 7 |
27 | 24, 26 | bitr4i 186 | . . . . . 6 |
28 | 23, 27 | syl6rbbr 198 | . . . . 5 |
29 | df-rex 2422 | . . . . 5 | |
30 | 28, 29 | syl6bbr 197 | . . . 4 |
31 | 30 | rexbidv 2438 | . . 3 |
32 | 18, 31 | bitrd 187 | . 2 |
33 | 32 | rabbidv 2675 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 962 wceq 1331 wex 1468 wcel 1480 wrex 2417 crab 2420 (class class class)co 5774 cnq 7088 |
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-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-11 1484 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-ral 2421 df-rex 2422 df-rab 2425 |
This theorem is referenced by: genpdf 7316 |
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