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Mirrors > Home > MPE Home > Th. List > fpwwecbv | Structured version Visualization version Unicode version |
Description: Lemma for fpwwe 9089. (Contributed by Mario Carneiro, 15-May-2015.) |
Ref | Expression |
---|---|
fpwwe.1 |
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Ref | Expression |
---|---|
fpwwecbv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fpwwe.1 |
. 2
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2 | simpl 464 |
. . . . . 6
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3 | 2 | sseq1d 3445 |
. . . . 5
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4 | simpr 468 |
. . . . . 6
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5 | 2 | sqxpeqd 4865 |
. . . . . 6
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6 | 4, 5 | sseq12d 3447 |
. . . . 5
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7 | 3, 6 | anbi12d 725 |
. . . 4
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8 | weeq2 4828 |
. . . . . 6
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9 | weeq1 4827 |
. . . . . 6
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10 | 8, 9 | sylan9bb 714 |
. . . . 5
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11 | sneq 3969 |
. . . . . . . . . 10
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12 | 11 | imaeq2d 5174 |
. . . . . . . . 9
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13 | 12 | fveq2d 5883 |
. . . . . . . 8
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14 | id 22 |
. . . . . . . 8
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15 | 13, 14 | eqeq12d 2486 |
. . . . . . 7
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16 | 15 | cbvralv 3005 |
. . . . . 6
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17 | 4 | cnveqd 5015 |
. . . . . . . . . 10
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18 | 17 | imaeq1d 5173 |
. . . . . . . . 9
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19 | 18 | fveq2d 5883 |
. . . . . . . 8
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20 | 19 | eqeq1d 2473 |
. . . . . . 7
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21 | 2, 20 | raleqbidv 2987 |
. . . . . 6
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22 | 16, 21 | syl5bb 265 |
. . . . 5
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23 | 10, 22 | anbi12d 725 |
. . . 4
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24 | 7, 23 | anbi12d 725 |
. . 3
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25 | 24 | cbvopabv 4465 |
. 2
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26 | 1, 25 | eqtri 2493 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-10 1932 ax-11 1937 ax-12 1950 ax-13 2104 ax-ext 2451 |
This theorem depends on definitions: df-bi 190 df-or 377 df-an 378 df-3or 1008 df-3an 1009 df-tru 1455 df-ex 1672 df-nf 1676 df-sb 1806 df-clab 2458 df-cleq 2464 df-clel 2467 df-nfc 2601 df-ral 2761 df-rex 2762 df-rab 2765 df-v 3033 df-dif 3393 df-un 3395 df-in 3397 df-ss 3404 df-nul 3723 df-if 3873 df-sn 3960 df-pr 3962 df-op 3966 df-uni 4191 df-br 4396 df-opab 4455 df-po 4760 df-so 4761 df-fr 4798 df-we 4800 df-xp 4845 df-cnv 4847 df-dm 4849 df-rn 4850 df-res 4851 df-ima 4852 df-iota 5553 df-fv 5597 |
This theorem is referenced by: canthnum 9092 canthp1 9097 |
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