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Mirrors > Home > ILE Home > Th. List > genpdflem | Unicode version |
Description: Simplification of upper or lower cut expression. Lemma for genpdf 7440. (Contributed by Jim Kingdon, 30-Sep-2019.) |
Ref | Expression |
---|---|
genpdflem.r | |
genpdflem.s |
Ref | Expression |
---|---|
genpdflem |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3anass 971 | . . . . . . . . . 10 | |
2 | 1 | rexbii 2471 | . . . . . . . . 9 |
3 | r19.42v 2621 | . . . . . . . . 9 | |
4 | 2, 3 | bitri 183 | . . . . . . . 8 |
5 | 4 | rexbii 2471 | . . . . . . 7 |
6 | df-rex 2448 | . . . . . . 7 | |
7 | 5, 6 | bitri 183 | . . . . . 6 |
8 | anass 399 | . . . . . . 7 | |
9 | 8 | exbii 1592 | . . . . . 6 |
10 | 7, 9 | bitr4i 186 | . . . . 5 |
11 | genpdflem.r | . . . . . . . . 9 | |
12 | 11 | ex 114 | . . . . . . . 8 |
13 | 12 | pm4.71rd 392 | . . . . . . 7 |
14 | 13 | anbi1d 461 | . . . . . 6 |
15 | 14 | exbidv 1812 | . . . . 5 |
16 | 10, 15 | bitr4id 198 | . . . 4 |
17 | df-rex 2448 | . . . 4 | |
18 | 16, 17 | bitr4di 197 | . . 3 |
19 | df-rex 2448 | . . . . . . 7 | |
20 | anass 399 | . . . . . . . 8 | |
21 | 20 | exbii 1592 | . . . . . . 7 |
22 | 19, 21 | bitr4i 186 | . . . . . 6 |
23 | genpdflem.s | . . . . . . . . . 10 | |
24 | 23 | ex 114 | . . . . . . . . 9 |
25 | 24 | pm4.71rd 392 | . . . . . . . 8 |
26 | 25 | anbi1d 461 | . . . . . . 7 |
27 | 26 | exbidv 1812 | . . . . . 6 |
28 | 22, 27 | bitr4id 198 | . . . . 5 |
29 | df-rex 2448 | . . . . 5 | |
30 | 28, 29 | bitr4di 197 | . . . 4 |
31 | 30 | rexbidv 2465 | . . 3 |
32 | 18, 31 | bitrd 187 | . 2 |
33 | 32 | rabbidv 2710 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 967 wceq 1342 wex 1479 wcel 2135 wrex 2443 crab 2446 (class class class)co 5836 cnq 7212 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-11 1493 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-ral 2447 df-rex 2448 df-rab 2451 |
This theorem is referenced by: genpdf 7440 |
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