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Mirrors > Home > ILE Home > Th. List > fvmptt | Unicode version |
Description: Closed theorem form of fvmpt 5614. (Contributed by Scott Fenton, 21-Feb-2013.) (Revised by Mario Carneiro, 11-Sep-2015.) |
Ref | Expression |
---|---|
fvmptt |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp2 1000 |
. . 3
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2 | 1 | fveq1d 5536 |
. 2
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3 | risset 2518 |
. . . . 5
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4 | elex 2763 |
. . . . . 6
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5 | nfa1 1552 |
. . . . . . 7
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6 | nfv 1539 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() | |
7 | nffvmpt1 5545 |
. . . . . . . . 9
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8 | 7 | nfeq1 2342 |
. . . . . . . 8
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9 | 6, 8 | nfim 1583 |
. . . . . . 7
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10 | simprl 529 |
. . . . . . . . . . . . 13
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11 | simplr 528 |
. . . . . . . . . . . . . 14
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12 | simprr 531 |
. . . . . . . . . . . . . 14
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13 | 11, 12 | eqeltrd 2266 |
. . . . . . . . . . . . 13
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14 | eqid 2189 |
. . . . . . . . . . . . . 14
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15 | 14 | fvmpt2 5620 |
. . . . . . . . . . . . 13
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16 | 10, 13, 15 | syl2anc 411 |
. . . . . . . . . . . 12
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17 | simpll 527 |
. . . . . . . . . . . . 13
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18 | 17 | fveq2d 5538 |
. . . . . . . . . . . 12
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19 | 16, 18, 11 | 3eqtr3d 2230 |
. . . . . . . . . . 11
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20 | 19 | exp43 372 |
. . . . . . . . . 10
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21 | 20 | a2i 11 |
. . . . . . . . 9
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22 | 21 | com23 78 |
. . . . . . . 8
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23 | 22 | sps 1548 |
. . . . . . 7
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24 | 5, 9, 23 | rexlimd 2604 |
. . . . . 6
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25 | 4, 24 | syl7 69 |
. . . . 5
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26 | 3, 25 | biimtrid 152 |
. . . 4
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27 | 26 | imp32 257 |
. . 3
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28 | 27 | 3adant2 1018 |
. 2
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29 | 2, 28 | eqtrd 2222 |
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 4136 ax-pow 4192 ax-pr 4227 |
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-csb 3073 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-br 4019 df-opab 4080 df-mpt 4081 df-id 4311 df-xp 4650 df-rel 4651 df-cnv 4652 df-co 4653 df-dm 4654 df-iota 5196 df-fun 5237 df-fv 5243 |
This theorem is referenced by: (None) |
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