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Mirrors > Home > ILE Home > Th. List > cnvf1olem | Unicode version |
Description: Lemma for cnvf1o 6219. (Contributed by Mario Carneiro, 27-Apr-2014.) |
Ref | Expression |
---|---|
cnvf1olem |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simprr 531 |
. . . 4
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2 | 1st2nd 6175 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | 2 | adantrr 479 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4 | 3 | sneqd 3604 |
. . . . . 6
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5 | 4 | cnveqd 4798 |
. . . . 5
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6 | 5 | unieqd 3818 |
. . . 4
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7 | 1stexg 6161 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
8 | 2ndexg 6162 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
9 | opswapg 5110 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
10 | 7, 8, 9 | syl2anc 411 |
. . . . 5
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11 | 10 | ad2antrl 490 |
. . . 4
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12 | 1, 6, 11 | 3eqtrd 2214 |
. . 3
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13 | simprl 529 |
. . . . 5
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14 | 3, 13 | eqeltrrd 2255 |
. . . 4
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15 | opelcnvg 4802 |
. . . . . 6
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16 | 8, 7, 15 | syl2anc 411 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
17 | 16 | ad2antrl 490 |
. . . 4
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18 | 14, 17 | mpbird 167 |
. . 3
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19 | 12, 18 | eqeltrd 2254 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
20 | opswapg 5110 |
. . . . . 6
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21 | 8, 7, 20 | syl2anc 411 |
. . . . 5
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22 | 21 | eqcomd 2183 |
. . . 4
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23 | 22 | ad2antrl 490 |
. . 3
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24 | 12 | sneqd 3604 |
. . . . 5
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25 | 24 | cnveqd 4798 |
. . . 4
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26 | 25 | unieqd 3818 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
27 | 23, 3, 26 | 3eqtr4d 2220 |
. 2
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28 | 19, 27 | jca 306 |
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-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4118 ax-pow 4171 ax-pr 4205 ax-un 4429 |
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-ral 2460 df-rex 2461 df-v 2739 df-sbc 2963 df-un 3133 df-in 3135 df-ss 3142 df-pw 3576 df-sn 3597 df-pr 3598 df-op 3600 df-uni 3808 df-br 4001 df-opab 4062 df-mpt 4063 df-id 4289 df-xp 4628 df-rel 4629 df-cnv 4630 df-co 4631 df-dm 4632 df-rn 4633 df-iota 5173 df-fun 5213 df-fn 5214 df-f 5215 df-fo 5217 df-fv 5219 df-1st 6134 df-2nd 6135 |
This theorem is referenced by: cnvf1o 6219 |
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