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Mirrors > Home > ILE Home > Th. List > 6p5lem | Unicode version |
Description: Lemma for 6p5e11 9222 and related theorems. (Contributed by Mario Carneiro, 19-Apr-2015.) |
Ref | Expression |
---|---|
6p5lem.1 | |
6p5lem.2 | |
6p5lem.3 | |
6p5lem.4 | |
6p5lem.5 | |
6p5lem.6 | ; |
Ref | Expression |
---|---|
6p5lem | ; |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 6p5lem.4 | . . 3 | |
2 | 1 | oveq2i 5753 | . 2 |
3 | 6p5lem.1 | . . . 4 | |
4 | 3 | nn0cni 8957 | . . 3 |
5 | 6p5lem.2 | . . . 4 | |
6 | 5 | nn0cni 8957 | . . 3 |
7 | ax-1cn 7681 | . . 3 | |
8 | 4, 6, 7 | addassi 7742 | . 2 |
9 | 1nn0 8961 | . . 3 | |
10 | 6p5lem.3 | . . 3 | |
11 | 6p5lem.5 | . . . 4 | |
12 | 11 | eqcomi 2121 | . . 3 |
13 | 6p5lem.6 | . . 3 ; | |
14 | 9, 10, 12, 13 | decsuc 9180 | . 2 ; |
15 | 2, 8, 14 | 3eqtr2i 2144 | 1 ; |
Colors of variables: wff set class |
Syntax hints: wceq 1316 wcel 1465 (class class class)co 5742 c1 7589 caddc 7591 cn0 8945 ;cdc 9150 |
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-in1 588 ax-in2 589 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-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 ax-setind 4422 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-addcom 7688 ax-mulcom 7689 ax-addass 7690 ax-mulass 7691 ax-distr 7692 ax-i2m1 7693 ax-1rid 7695 ax-0id 7696 ax-rnegex 7697 ax-cnre 7699 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-fal 1322 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ne 2286 df-ral 2398 df-rex 2399 df-reu 2400 df-rab 2402 df-v 2662 df-sbc 2883 df-dif 3043 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-int 3742 df-br 3900 df-opab 3960 df-id 4185 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-iota 5058 df-fun 5095 df-fv 5101 df-riota 5698 df-ov 5745 df-oprab 5746 df-mpo 5747 df-sub 7903 df-inn 8689 df-2 8747 df-3 8748 df-4 8749 df-5 8750 df-6 8751 df-7 8752 df-8 8753 df-9 8754 df-n0 8946 df-dec 9151 |
This theorem is referenced by: 6p5e11 9222 6p6e12 9223 7p4e11 9225 7p5e12 9226 7p6e13 9227 7p7e14 9228 8p3e11 9230 8p4e12 9231 8p5e13 9232 8p6e14 9233 8p7e15 9234 8p8e16 9235 9p2e11 9236 9p3e12 9237 9p4e13 9238 9p5e14 9239 9p6e15 9240 9p7e16 9241 9p8e17 9242 9p9e18 9243 |
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