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Mirrors > Home > ILE Home > Th. List > funimass4 | Unicode version |
Description: Membership relation for the values of a function whose image is a subclass. (Contributed by Raph Levien, 20-Nov-2006.) |
Ref | Expression |
---|---|
funimass4 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfss2 3159 |
. 2
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2 | vex 2755 |
. . . . . . . . 9
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3 | 2 | elima 4996 |
. . . . . . . 8
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4 | eqcom 2191 |
. . . . . . . . . 10
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5 | ssel 3164 |
. . . . . . . . . . . 12
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6 | funbrfvb 5582 |
. . . . . . . . . . . . 13
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | 6 | ex 115 |
. . . . . . . . . . . 12
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8 | 5, 7 | syl9 72 |
. . . . . . . . . . 11
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9 | 8 | imp31 256 |
. . . . . . . . . 10
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10 | 4, 9 | bitrid 192 |
. . . . . . . . 9
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11 | 10 | rexbidva 2487 |
. . . . . . . 8
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12 | 3, 11 | bitr4id 199 |
. . . . . . 7
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13 | 12 | imbi1d 231 |
. . . . . 6
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14 | r19.23v 2599 |
. . . . . 6
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15 | 13, 14 | bitr4di 198 |
. . . . 5
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16 | 15 | albidv 1835 |
. . . 4
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17 | 16 | ancoms 268 |
. . 3
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18 | ralcom4 2774 |
. . . 4
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19 | ssel2 3165 |
. . . . . . . . 9
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20 | 19 | anim2i 342 |
. . . . . . . 8
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21 | 20 | 3impb 1201 |
. . . . . . 7
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22 | funfvex 5554 |
. . . . . . 7
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23 | nfv 1539 |
. . . . . . . 8
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24 | eleq1 2252 |
. . . . . . . 8
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25 | 23, 24 | ceqsalg 2780 |
. . . . . . 7
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26 | 21, 22, 25 | 3syl 17 |
. . . . . 6
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27 | 26 | 3expa 1205 |
. . . . 5
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28 | 27 | ralbidva 2486 |
. . . 4
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29 | 18, 28 | bitr3id 194 |
. . 3
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30 | 17, 29 | bitrd 188 |
. 2
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31 | 1, 30 | bitrid 192 |
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-14 2163 ax-ext 2171 ax-sep 4139 ax-pow 4195 ax-pr 4230 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-sbc 2978 df-un 3148 df-in 3150 df-ss 3157 df-pw 3595 df-sn 3616 df-pr 3617 df-op 3619 df-uni 3828 df-br 4022 df-opab 4083 df-id 4314 df-xp 4653 df-rel 4654 df-cnv 4655 df-co 4656 df-dm 4657 df-rn 4658 df-res 4659 df-ima 4660 df-iota 5199 df-fun 5240 df-fn 5241 df-fv 5246 |
This theorem is referenced by: funimass3 5656 funimass5 5657 funconstss 5658 funimassov 6050 phimullem 12268 txcnp 14256 metcnp 14497 |
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