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Mirrors > Home > ILE Home > Th. List > 4t3lem | Unicode version |
Description: Lemma for 4t3e12 9303 and related theorems. (Contributed by Mario Carneiro, 19-Apr-2015.) |
Ref | Expression |
---|---|
4t3lem.1 |
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4t3lem.2 |
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4t3lem.3 |
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4t3lem.4 |
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4t3lem.5 |
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Ref | Expression |
---|---|
4t3lem |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 4t3lem.3 |
. . 3
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2 | 1 | oveq2i 5793 |
. 2
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3 | 4t3lem.1 |
. . . . . 6
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4 | 3 | nn0cni 9013 |
. . . . 5
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5 | 4t3lem.2 |
. . . . . 6
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6 | 5 | nn0cni 9013 |
. . . . 5
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7 | ax-1cn 7737 |
. . . . 5
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8 | 4, 6, 7 | adddii 7800 |
. . . 4
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9 | 4t3lem.4 |
. . . . 5
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10 | 4 | mulid1i 7792 |
. . . . 5
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11 | 9, 10 | oveq12i 5794 |
. . . 4
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12 | 8, 11 | eqtri 2161 |
. . 3
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13 | 4t3lem.5 |
. . 3
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14 | 12, 13 | eqtri 2161 |
. 2
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15 | 2, 14 | eqtri 2161 |
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 ax-sep 4054 ax-cnex 7735 ax-resscn 7736 ax-1cn 7737 ax-1re 7738 ax-icn 7739 ax-addcl 7740 ax-addrcl 7741 ax-mulcl 7742 ax-mulcom 7745 ax-mulass 7747 ax-distr 7748 ax-1rid 7751 ax-rnegex 7753 ax-cnre 7755 |
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-ral 2422 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-int 3780 df-br 3938 df-iota 5096 df-fv 5139 df-ov 5785 df-inn 8745 df-n0 9002 |
This theorem is referenced by: 4t3e12 9303 4t4e16 9304 5t2e10 9305 5t3e15 9306 5t4e20 9307 5t5e25 9308 6t3e18 9310 6t4e24 9311 6t5e30 9312 6t6e36 9313 7t3e21 9315 7t4e28 9316 7t5e35 9317 7t6e42 9318 7t7e49 9319 8t3e24 9321 8t4e32 9322 8t5e40 9323 8t6e48 9324 8t7e56 9325 8t8e64 9326 9t3e27 9328 9t4e36 9329 9t5e45 9330 9t6e54 9331 9t7e63 9332 9t8e72 9333 9t9e81 9334 |
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