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Mirrors > Home > ILE Home > Th. List > 6p5lem | Unicode version |
Description: Lemma for 6p5e11 9452 and related theorems. (Contributed by Mario Carneiro, 19-Apr-2015.) |
Ref | Expression |
---|---|
6p5lem.1 |
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6p5lem.2 |
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6p5lem.3 |
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6p5lem.4 |
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6p5lem.5 |
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6p5lem.6 |
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Ref | Expression |
---|---|
6p5lem |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 6p5lem.4 |
. . 3
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2 | 1 | oveq2i 5883 |
. 2
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3 | 6p5lem.1 |
. . . 4
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4 | 3 | nn0cni 9184 |
. . 3
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5 | 6p5lem.2 |
. . . 4
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6 | 5 | nn0cni 9184 |
. . 3
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7 | ax-1cn 7901 |
. . 3
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8 | 4, 6, 7 | addassi 7962 |
. 2
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9 | 1nn0 9188 |
. . 3
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10 | 6p5lem.3 |
. . 3
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11 | 6p5lem.5 |
. . . 4
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12 | 11 | eqcomi 2181 |
. . 3
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13 | 6p5lem.6 |
. . 3
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14 | 9, 10, 12, 13 | decsuc 9410 |
. 2
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15 | 2, 8, 14 | 3eqtr2i 2204 |
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 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4120 ax-pow 4173 ax-pr 4208 ax-setind 4535 ax-cnex 7899 ax-resscn 7900 ax-1cn 7901 ax-1re 7902 ax-icn 7903 ax-addcl 7904 ax-addrcl 7905 ax-mulcl 7906 ax-addcom 7908 ax-mulcom 7909 ax-addass 7910 ax-mulass 7911 ax-distr 7912 ax-i2m1 7913 ax-1rid 7915 ax-0id 7916 ax-rnegex 7917 ax-cnre 7919 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-ral 2460 df-rex 2461 df-reu 2462 df-rab 2464 df-v 2739 df-sbc 2963 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-int 3845 df-br 4003 df-opab 4064 df-id 4292 df-xp 4631 df-rel 4632 df-cnv 4633 df-co 4634 df-dm 4635 df-iota 5177 df-fun 5217 df-fv 5223 df-riota 5828 df-ov 5875 df-oprab 5876 df-mpo 5877 df-sub 8126 df-inn 8916 df-2 8974 df-3 8975 df-4 8976 df-5 8977 df-6 8978 df-7 8979 df-8 8980 df-9 8981 df-n0 9173 df-dec 9381 |
This theorem is referenced by: 6p5e11 9452 6p6e12 9453 7p4e11 9455 7p5e12 9456 7p6e13 9457 7p7e14 9458 8p3e11 9460 8p4e12 9461 8p5e13 9462 8p6e14 9463 8p7e15 9464 8p8e16 9465 9p2e11 9466 9p3e12 9467 9p4e13 9468 9p5e14 9469 9p6e15 9470 9p7e16 9471 9p8e17 9472 9p9e18 9473 |
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