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Mirrors > Home > ILE Home > Th. List > pitonnlem1 | Unicode version |
Description: Lemma for pitonn 7680. 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 7652 |
. 2
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2 | df-1r 7564 |
. . . 4
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3 | df-i1p 7299 |
. . . . . . . 8
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4 | df-1nqqs 7183 |
. . . . . . . . . . 11
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5 | 4 | breq2i 3945 |
. . . . . . . . . 10
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6 | 5 | abbii 2256 |
. . . . . . . . 9
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7 | 4 | breq1i 3944 |
. . . . . . . . . 10
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8 | 7 | abbii 2256 |
. . . . . . . . 9
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9 | 6, 8 | opeq12i 3718 |
. . . . . . . 8
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10 | 3, 9 | eqtri 2161 |
. . . . . . 7
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11 | 10 | oveq1i 5792 |
. . . . . 6
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12 | 11 | opeq1i 3716 |
. . . . 5
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13 | eceq1 6472 |
. . . . 5
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14 | 12, 13 | ax-mp 5 |
. . . 4
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15 | 2, 14 | eqtri 2161 |
. . 3
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16 | 15 | opeq1i 3716 |
. 2
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17 | 1, 16 | eqtr2i 2162 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-rex 2423 df-v 2691 df-un 3080 df-in 3082 df-ss 3089 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-br 3938 df-opab 3998 df-xp 4553 df-cnv 4555 df-dm 4557 df-rn 4558 df-res 4559 df-ima 4560 df-iota 5096 df-fv 5139 df-ov 5785 df-ec 6439 df-1nqqs 7183 df-i1p 7299 df-1r 7564 df-1 7652 |
This theorem is referenced by: pitonn 7680 |
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