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Mirrors > Home > ILE Home > Th. List > 4t3lem | Unicode version |
Description: Lemma for 4t3e12 9247 and related theorems. (Contributed by Mario Carneiro, 19-Apr-2015.) |
Ref | Expression |
---|---|
4t3lem.1 | |
4t3lem.2 | |
4t3lem.3 | |
4t3lem.4 | |
4t3lem.5 |
Ref | Expression |
---|---|
4t3lem |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 4t3lem.3 | . . 3 | |
2 | 1 | oveq2i 5753 | . 2 |
3 | 4t3lem.1 | . . . . . 6 | |
4 | 3 | nn0cni 8957 | . . . . 5 |
5 | 4t3lem.2 | . . . . . 6 | |
6 | 5 | nn0cni 8957 | . . . . 5 |
7 | ax-1cn 7681 | . . . . 5 | |
8 | 4, 6, 7 | adddii 7744 | . . . 4 |
9 | 4t3lem.4 | . . . . 5 | |
10 | 4 | mulid1i 7736 | . . . . 5 |
11 | 9, 10 | oveq12i 5754 | . . . 4 |
12 | 8, 11 | eqtri 2138 | . . 3 |
13 | 4t3lem.5 | . . 3 | |
14 | 12, 13 | eqtri 2138 | . 2 |
15 | 2, 14 | eqtri 2138 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1316 wcel 1465 (class class class)co 5742 c1 7589 caddc 7591 cmul 7593 cn0 8945 |
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 ax-sep 4016 ax-cnex 7679 ax-resscn 7680 ax-1cn 7681 ax-1re 7682 ax-icn 7683 ax-addcl 7684 ax-addrcl 7685 ax-mulcl 7686 ax-mulcom 7689 ax-mulass 7691 ax-distr 7692 ax-1rid 7695 ax-rnegex 7697 ax-cnre 7699 |
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-ral 2398 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-int 3742 df-br 3900 df-iota 5058 df-fv 5101 df-ov 5745 df-inn 8689 df-n0 8946 |
This theorem is referenced by: 4t3e12 9247 4t4e16 9248 5t2e10 9249 5t3e15 9250 5t4e20 9251 5t5e25 9252 6t3e18 9254 6t4e24 9255 6t5e30 9256 6t6e36 9257 7t3e21 9259 7t4e28 9260 7t5e35 9261 7t6e42 9262 7t7e49 9263 8t3e24 9265 8t4e32 9266 8t5e40 9267 8t6e48 9268 8t7e56 9269 8t8e64 9270 9t3e27 9272 9t4e36 9273 9t5e45 9274 9t6e54 9275 9t7e63 9276 9t8e72 9277 9t9e81 9278 |
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