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Mirrors > Home > ILE Home > Th. List > pitonnlem1 | Unicode version |
Description: Lemma for pitonn 7448. Two ways to write the number one. (Contributed by Jim Kingdon, 24-Apr-2020.) |
Ref | Expression |
---|---|
pitonnlem1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-1 7421 |
. 2
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2 | df-1r 7341 |
. . . 4
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3 | df-i1p 7089 |
. . . . . . . 8
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4 | df-1nqqs 6973 |
. . . . . . . . . . 11
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5 | 4 | breq2i 3861 |
. . . . . . . . . 10
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6 | 5 | abbii 2204 |
. . . . . . . . 9
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7 | 4 | breq1i 3860 |
. . . . . . . . . 10
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8 | 7 | abbii 2204 |
. . . . . . . . 9
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9 | 6, 8 | opeq12i 3635 |
. . . . . . . 8
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10 | 3, 9 | eqtri 2109 |
. . . . . . 7
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11 | 10 | oveq1i 5678 |
. . . . . 6
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12 | 11 | opeq1i 3633 |
. . . . 5
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13 | eceq1 6343 |
. . . . 5
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14 | 12, 13 | ax-mp 7 |
. . . 4
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15 | 2, 14 | eqtri 2109 |
. . 3
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16 | 15 | opeq1i 3633 |
. 2
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17 | 1, 16 | eqtr2i 2110 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-rex 2366 df-v 2624 df-un 3006 df-in 3008 df-ss 3015 df-sn 3458 df-pr 3459 df-op 3461 df-uni 3662 df-br 3854 df-opab 3908 df-xp 4460 df-cnv 4462 df-dm 4464 df-rn 4465 df-res 4466 df-ima 4467 df-iota 4995 df-fv 5038 df-ov 5671 df-ec 6310 df-1nqqs 6973 df-i1p 7089 df-1r 7341 df-1 7421 |
This theorem is referenced by: pitonn 7448 |
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