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Mirrors > Home > ILE Home > Th. List > fvmptdf | Unicode version |
Description: Alternate deduction version of fvmpt 5381, 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 1466 |
. 2
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2 | fvmptdf.4 |
. . . 4
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3 | nfmpt1 3931 |
. . . 4
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4 | 2, 3 | nfeq 2236 |
. . 3
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5 | fvmptdf.5 |
. . 3
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6 | 4, 5 | nfim 1509 |
. 2
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7 | fvmptdf.1 |
. . . 4
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8 | elex 2630 |
. . . 4
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9 | 7, 8 | syl 14 |
. . 3
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10 | isset 2625 |
. . 3
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11 | 9, 10 | sylib 120 |
. 2
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12 | fveq1 5304 |
. . 3
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13 | simpr 108 |
. . . . . . 7
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14 | 13 | fveq2d 5309 |
. . . . . 6
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15 | 7 | adantr 270 |
. . . . . . . 8
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16 | 13, 15 | eqeltrd 2164 |
. . . . . . 7
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17 | fvmptdf.2 |
. . . . . . 7
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18 | eqid 2088 |
. . . . . . . 8
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19 | 18 | fvmpt2 5386 |
. . . . . . 7
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20 | 16, 17, 19 | syl2anc 403 |
. . . . . 6
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21 | 14, 20 | eqtr3d 2122 |
. . . . 5
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22 | 21 | eqeq2d 2099 |
. . . 4
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23 | fvmptdf.3 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
24 | 22, 23 | sylbid 148 |
. . 3
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25 | 12, 24 | syl5 32 |
. 2
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26 | 1, 6, 11, 25 | exlimdd 1800 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-14 1450 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 ax-sep 3957 ax-pow 4009 ax-pr 4036 |
This theorem depends on definitions: df-bi 115 df-3an 926 df-tru 1292 df-nf 1395 df-sb 1693 df-eu 1951 df-mo 1952 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-ral 2364 df-rex 2365 df-v 2621 df-sbc 2841 df-csb 2934 df-un 3003 df-in 3005 df-ss 3012 df-pw 3431 df-sn 3452 df-pr 3453 df-op 3455 df-uni 3654 df-br 3846 df-opab 3900 df-mpt 3901 df-id 4120 df-xp 4444 df-rel 4445 df-cnv 4446 df-co 4447 df-dm 4448 df-iota 4980 df-fun 5017 df-fv 5023 |
This theorem is referenced by: fvmptdv 5391 |
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