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Mirrors > Home > ILE Home > Th. List > 4t3lem | Unicode version |
Description: Lemma for 4t3e12 9510 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 5906 |
. 2
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3 | 4t3lem.1 |
. . . . . 6
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4 | 3 | nn0cni 9217 |
. . . . 5
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5 | 4t3lem.2 |
. . . . . 6
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6 | 5 | nn0cni 9217 |
. . . . 5
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7 | ax-1cn 7933 |
. . . . 5
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8 | 4, 6, 7 | adddii 7996 |
. . . 4
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9 | 4t3lem.4 |
. . . . 5
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10 | 4 | mulid1i 7988 |
. . . . 5
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11 | 9, 10 | oveq12i 5907 |
. . . 4
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12 | 8, 11 | eqtri 2210 |
. . 3
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13 | 4t3lem.5 |
. . 3
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14 | 12, 13 | eqtri 2210 |
. 2
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15 | 2, 14 | eqtri 2210 |
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-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 ax-sep 4136 ax-cnex 7931 ax-resscn 7932 ax-1cn 7933 ax-1re 7934 ax-icn 7935 ax-addcl 7936 ax-addrcl 7937 ax-mulcl 7938 ax-mulcom 7941 ax-mulass 7943 ax-distr 7944 ax-1rid 7947 ax-rnegex 7949 ax-cnre 7951 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-int 3860 df-br 4019 df-iota 5196 df-fv 5243 df-ov 5898 df-inn 8949 df-n0 9206 |
This theorem is referenced by: 4t3e12 9510 4t4e16 9511 5t2e10 9512 5t3e15 9513 5t4e20 9514 5t5e25 9515 6t3e18 9517 6t4e24 9518 6t5e30 9519 6t6e36 9520 7t3e21 9522 7t4e28 9523 7t5e35 9524 7t6e42 9525 7t7e49 9526 8t3e24 9528 8t4e32 9529 8t5e40 9530 8t6e48 9531 8t7e56 9532 8t8e64 9533 9t3e27 9535 9t4e36 9536 9t5e45 9537 9t6e54 9538 9t7e63 9539 9t8e72 9540 9t9e81 9541 |
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