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Mirrors > Home > ILE Home > Th. List > eqerlem | Unicode version |
Description: Lemma for eqer 6566. (Contributed by NM, 17-Mar-2008.) (Proof shortened by Mario Carneiro, 6-Dec-2016.) |
Ref | Expression |
---|---|
eqer.1 |
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eqer.2 |
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Ref | Expression |
---|---|
eqerlem |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqer.2 |
. . 3
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2 | 1 | brabsb 4261 |
. 2
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3 | vex 2740 |
. . 3
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4 | nfcsb1v 3090 |
. . . . 5
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5 | nfcsb1v 3090 |
. . . . 5
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6 | 4, 5 | nfeq 2327 |
. . . 4
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7 | vex 2740 |
. . . . . 6
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8 | nfv 1528 |
. . . . . . 7
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9 | vex 2740 |
. . . . . . . . . 10
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10 | nfcv 2319 |
. . . . . . . . . 10
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11 | eqer.1 |
. . . . . . . . . 10
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12 | 9, 10, 11 | csbief 3101 |
. . . . . . . . 9
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13 | csbeq1 3060 |
. . . . . . . . 9
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14 | 12, 13 | eqtr3id 2224 |
. . . . . . . 8
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15 | 14 | eqeq2d 2189 |
. . . . . . 7
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16 | 8, 15 | sbciegf 2994 |
. . . . . 6
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17 | 7, 16 | ax-mp 5 |
. . . . 5
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18 | csbeq1a 3066 |
. . . . . 6
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19 | 18 | eqeq1d 2186 |
. . . . 5
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20 | 17, 19 | bitrid 192 |
. . . 4
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21 | 6, 20 | sbciegf 2994 |
. . 3
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22 | 3, 21 | ax-mp 5 |
. 2
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23 | 2, 22 | bitri 184 |
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-14 2151 ax-ext 2159 ax-sep 4121 ax-pow 4174 ax-pr 4209 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 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-rex 2461 df-v 2739 df-sbc 2963 df-csb 3058 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-br 4004 df-opab 4065 |
This theorem is referenced by: eqer 6566 |
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