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Mirrors > Home > ILE Home > Th. List > caovdilemd | Unicode version |
Description: Lemma used by real number construction. (Contributed by Jim Kingdon, 16-Sep-2019.) |
Ref | Expression |
---|---|
caovdilemd.com |
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caovdilemd.distr |
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caovdilemd.ass |
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caovdilemd.cl |
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caovdilemd.a |
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caovdilemd.b |
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caovdilemd.c |
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caovdilemd.d |
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caovdilemd.h |
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Ref | Expression |
---|---|
caovdilemd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | caovdilemd.distr |
. . 3
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2 | caovdilemd.cl |
. . . 4
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3 | caovdilemd.a |
. . . 4
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4 | caovdilemd.c |
. . . 4
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5 | 2, 3, 4 | caovcld 6022 |
. . 3
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6 | caovdilemd.b |
. . . 4
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7 | caovdilemd.d |
. . . 4
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8 | 2, 6, 7 | caovcld 6022 |
. . 3
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9 | caovdilemd.h |
. . 3
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10 | 1, 5, 8, 9 | caovdird 6047 |
. 2
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11 | caovdilemd.ass |
. . . 4
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12 | 11, 3, 4, 9 | caovassd 6028 |
. . 3
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13 | 11, 6, 7, 9 | caovassd 6028 |
. . 3
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14 | 12, 13 | oveq12d 5887 |
. 2
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15 | 10, 14 | eqtrd 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 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-ext 2159 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-v 2739 df-un 3133 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-br 4001 df-iota 5174 df-fv 5220 df-ov 5872 |
This theorem is referenced by: caovlem2d 6061 addassnqg 7369 addassnq0 7449 axmulass 7860 |
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