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Mirrors > Home > ILE Home > Th. List > 6p5lem | Unicode version |
Description: Lemma for 6p5e11 9385 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 5847 | . 2 |
3 | 6p5lem.1 | . . . 4 | |
4 | 3 | nn0cni 9117 | . . 3 |
5 | 6p5lem.2 | . . . 4 | |
6 | 5 | nn0cni 9117 | . . 3 |
7 | ax-1cn 7837 | . . 3 | |
8 | 4, 6, 7 | addassi 7898 | . 2 |
9 | 1nn0 9121 | . . 3 | |
10 | 6p5lem.3 | . . 3 | |
11 | 6p5lem.5 | . . . 4 | |
12 | 11 | eqcomi 2168 | . . 3 |
13 | 6p5lem.6 | . . 3 ; | |
14 | 9, 10, 12, 13 | decsuc 9343 | . 2 ; |
15 | 2, 8, 14 | 3eqtr2i 2191 | 1 ; |
Colors of variables: wff set class |
Syntax hints: wceq 1342 wcel 2135 (class class class)co 5836 c1 7745 caddc 7747 cn0 9105 ;cdc 9313 |
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 604 ax-in2 605 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 ax-setind 4508 ax-cnex 7835 ax-resscn 7836 ax-1cn 7837 ax-1re 7838 ax-icn 7839 ax-addcl 7840 ax-addrcl 7841 ax-mulcl 7842 ax-addcom 7844 ax-mulcom 7845 ax-addass 7846 ax-mulass 7847 ax-distr 7848 ax-i2m1 7849 ax-1rid 7851 ax-0id 7852 ax-rnegex 7853 ax-cnre 7855 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-fal 1348 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ne 2335 df-ral 2447 df-rex 2448 df-reu 2449 df-rab 2451 df-v 2723 df-sbc 2947 df-dif 3113 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-int 3819 df-br 3977 df-opab 4038 df-id 4265 df-xp 4604 df-rel 4605 df-cnv 4606 df-co 4607 df-dm 4608 df-iota 5147 df-fun 5184 df-fv 5190 df-riota 5792 df-ov 5839 df-oprab 5840 df-mpo 5841 df-sub 8062 df-inn 8849 df-2 8907 df-3 8908 df-4 8909 df-5 8910 df-6 8911 df-7 8912 df-8 8913 df-9 8914 df-n0 9106 df-dec 9314 |
This theorem is referenced by: 6p5e11 9385 6p6e12 9386 7p4e11 9388 7p5e12 9389 7p6e13 9390 7p7e14 9391 8p3e11 9393 8p4e12 9394 8p5e13 9395 8p6e14 9396 8p7e15 9397 8p8e16 9398 9p2e11 9399 9p3e12 9400 9p4e13 9401 9p5e14 9402 9p6e15 9403 9p7e16 9404 9p8e17 9405 9p9e18 9406 |
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