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Mirrors > Home > ILE Home > Th. List > fvmptdf | Unicode version |
Description: Alternate deduction version of fvmpt 5614, suitable for iteration. (Contributed by Mario Carneiro, 7-Jan-2017.) |
Ref | Expression |
---|---|
fvmptdf.1 |
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fvmptdf.2 |
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fvmptdf.3 |
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fvmptdf.4 |
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fvmptdf.5 |
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Ref | Expression |
---|---|
fvmptdf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1539 |
. 2
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2 | fvmptdf.4 |
. . . 4
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3 | nfmpt1 4111 |
. . . 4
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4 | 2, 3 | nfeq 2340 |
. . 3
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5 | fvmptdf.5 |
. . 3
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6 | 4, 5 | nfim 1583 |
. 2
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7 | fvmptdf.1 |
. . . 4
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8 | elex 2763 |
. . . 4
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9 | 7, 8 | syl 14 |
. . 3
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10 | isset 2758 |
. . 3
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11 | 9, 10 | sylib 122 |
. 2
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12 | fveq1 5533 |
. . 3
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13 | simpr 110 |
. . . . . . 7
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14 | 13 | fveq2d 5538 |
. . . . . 6
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15 | 7 | adantr 276 |
. . . . . . . 8
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16 | 13, 15 | eqeltrd 2266 |
. . . . . . 7
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17 | fvmptdf.2 |
. . . . . . 7
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18 | eqid 2189 |
. . . . . . . 8
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19 | 18 | fvmpt2 5620 |
. . . . . . 7
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20 | 16, 17, 19 | syl2anc 411 |
. . . . . 6
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21 | 14, 20 | eqtr3d 2224 |
. . . . 5
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22 | 21 | eqeq2d 2201 |
. . . 4
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23 | fvmptdf.3 |
. . . 4
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24 | 22, 23 | sylbid 150 |
. . 3
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25 | 12, 24 | syl5 32 |
. 2
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26 | 1, 6, 11, 25 | exlimdd 1883 |
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: fvmptdv 5625 |
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