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Mirrors > Home > ILE Home > Th. List > fvmptt | Unicode version |
Description: Closed theorem form of fvmpt 5589. (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 998 |
. . 3
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2 | 1 | fveq1d 5513 |
. 2
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3 | risset 2505 |
. . . . 5
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4 | elex 2748 |
. . . . . 6
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5 | nfa1 1541 |
. . . . . . 7
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6 | nfv 1528 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() | |
7 | nffvmpt1 5522 |
. . . . . . . . 9
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8 | 7 | nfeq1 2329 |
. . . . . . . 8
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9 | 6, 8 | nfim 1572 |
. . . . . . 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 2254 |
. . . . . . . . . . . . 13
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14 | eqid 2177 |
. . . . . . . . . . . . . 14
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15 | 14 | fvmpt2 5595 |
. . . . . . . . . . . . 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 5515 |
. . . . . . . . . . . 12
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19 | 16, 18, 11 | 3eqtr3d 2218 |
. . . . . . . . . . 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 1537 |
. . . . . . 7
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24 | 5, 9, 23 | rexlimd 2591 |
. . . . . 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 1016 |
. 2
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29 | 2, 28 | eqtrd 2210 |
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 4118 ax-pow 4171 ax-pr 4206 |
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-csb 3058 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 4290 df-xp 4629 df-rel 4630 df-cnv 4631 df-co 4632 df-dm 4633 df-iota 5174 df-fun 5214 df-fv 5220 |
This theorem is referenced by: (None) |
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