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Mirrors > Home > ILE Home > Th. List > pitonnlem1 | Unicode version |
Description: Lemma for pitonn 6924. Two ways to write the number one. (Contributed by Jim Kingdon, 24-Apr-2020.) |
Ref | Expression |
---|---|
pitonnlem1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-1 6897 | . 2 | |
2 | df-1r 6817 | . . . 4 | |
3 | df-i1p 6565 | . . . . . . . 8 | |
4 | df-1nqqs 6449 | . . . . . . . . . . 11 | |
5 | 4 | breq2i 3772 | . . . . . . . . . 10 |
6 | 5 | abbii 2153 | . . . . . . . . 9 |
7 | 4 | breq1i 3771 | . . . . . . . . . 10 |
8 | 7 | abbii 2153 | . . . . . . . . 9 |
9 | 6, 8 | opeq12i 3554 | . . . . . . . 8 |
10 | 3, 9 | eqtri 2060 | . . . . . . 7 |
11 | 10 | oveq1i 5522 | . . . . . 6 |
12 | 11 | opeq1i 3552 | . . . . 5 |
13 | eceq1 6141 | . . . . 5 | |
14 | 12, 13 | ax-mp 7 | . . . 4 |
15 | 2, 14 | eqtri 2060 | . . 3 |
16 | 15 | opeq1i 3552 | . 2 |
17 | 1, 16 | eqtr2i 2061 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1243 cab 2026 cop 3378 class class class wbr 3764 (class class class)co 5512 c1o 5994 cec 6104 ceq 6377 c1q 6379 cltq 6383 c1p 6390 cpp 6391 cer 6394 c0r 6396 c1r 6397 c1 6890 |
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-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 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-clel 2036 df-nfc 2167 df-rex 2312 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-br 3765 df-opab 3819 df-xp 4351 df-cnv 4353 df-dm 4355 df-rn 4356 df-res 4357 df-ima 4358 df-iota 4867 df-fv 4910 df-ov 5515 df-ec 6108 df-1nqqs 6449 df-i1p 6565 df-1r 6817 df-1 6897 |
This theorem is referenced by: pitonn 6924 |
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