Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > pitonnlem1 | Unicode version |
Description: Lemma for pitonn 7016. Two ways to write the number one. (Contributed by Jim Kingdon, 24-Apr-2020.) |
Ref | Expression |
---|---|
pitonnlem1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-1 6989 | . 2 | |
2 | df-1r 6909 | . . . 4 | |
3 | df-i1p 6657 | . . . . . . . 8 | |
4 | df-1nqqs 6541 | . . . . . . . . . . 11 | |
5 | 4 | breq2i 3793 | . . . . . . . . . 10 |
6 | 5 | abbii 2194 | . . . . . . . . 9 |
7 | 4 | breq1i 3792 | . . . . . . . . . 10 |
8 | 7 | abbii 2194 | . . . . . . . . 9 |
9 | 6, 8 | opeq12i 3575 | . . . . . . . 8 |
10 | 3, 9 | eqtri 2101 | . . . . . . 7 |
11 | 10 | oveq1i 5542 | . . . . . 6 |
12 | 11 | opeq1i 3573 | . . . . 5 |
13 | eceq1 6164 | . . . . 5 | |
14 | 12, 13 | ax-mp 7 | . . . 4 |
15 | 2, 14 | eqtri 2101 | . . 3 |
16 | 15 | opeq1i 3573 | . 2 |
17 | 1, 16 | eqtr2i 2102 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1284 cab 2067 cop 3401 class class class wbr 3785 (class class class)co 5532 c1o 6017 cec 6127 ceq 6469 c1q 6471 cltq 6475 c1p 6482 cpp 6483 cer 6486 c0r 6488 c1r 6489 c1 6982 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-rex 2354 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-br 3786 df-opab 3840 df-xp 4369 df-cnv 4371 df-dm 4373 df-rn 4374 df-res 4375 df-ima 4376 df-iota 4887 df-fv 4930 df-ov 5535 df-ec 6131 df-1nqqs 6541 df-i1p 6657 df-1r 6909 df-1 6989 |
This theorem is referenced by: pitonn 7016 |
Copyright terms: Public domain | W3C validator |