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Mirrors > Home > ILE Home > Th. List > pitonnlem1 | Unicode version |
Description: Lemma for pitonn 7624. Two ways to write the number one. (Contributed by Jim Kingdon, 24-Apr-2020.) |
Ref | Expression |
---|---|
pitonnlem1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-1 7596 | . 2 | |
2 | df-1r 7508 | . . . 4 | |
3 | df-i1p 7243 | . . . . . . . 8 | |
4 | df-1nqqs 7127 | . . . . . . . . . . 11 | |
5 | 4 | breq2i 3907 | . . . . . . . . . 10 |
6 | 5 | abbii 2233 | . . . . . . . . 9 |
7 | 4 | breq1i 3906 | . . . . . . . . . 10 |
8 | 7 | abbii 2233 | . . . . . . . . 9 |
9 | 6, 8 | opeq12i 3680 | . . . . . . . 8 |
10 | 3, 9 | eqtri 2138 | . . . . . . 7 |
11 | 10 | oveq1i 5752 | . . . . . 6 |
12 | 11 | opeq1i 3678 | . . . . 5 |
13 | eceq1 6432 | . . . . 5 | |
14 | 12, 13 | ax-mp 5 | . . . 4 |
15 | 2, 14 | eqtri 2138 | . . 3 |
16 | 15 | opeq1i 3678 | . 2 |
17 | 1, 16 | eqtr2i 2139 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1316 cab 2103 cop 3500 class class class wbr 3899 (class class class)co 5742 c1o 6274 cec 6395 ceq 7055 c1q 7057 cltq 7061 c1p 7068 cpp 7069 cer 7072 c0r 7074 c1r 7075 c1 7589 |
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-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-rex 2399 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-xp 4515 df-cnv 4517 df-dm 4519 df-rn 4520 df-res 4521 df-ima 4522 df-iota 5058 df-fv 5101 df-ov 5745 df-ec 6399 df-1nqqs 7127 df-i1p 7243 df-1r 7508 df-1 7596 |
This theorem is referenced by: pitonn 7624 |
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