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Mirrors > Home > ILE Home > Th. List > fvmptd | Unicode version |
Description: Deduction version of fvmpt 5450. (Contributed by Scott Fenton, 18-Feb-2013.) (Revised by Mario Carneiro, 31-Aug-2015.) |
Ref | Expression |
---|---|
fvmptd.1 |
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fvmptd.2 |
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fvmptd.3 |
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fvmptd.4 |
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Ref | Expression |
---|---|
fvmptd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fvmptd.1 |
. . 3
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2 | 1 | fveq1d 5375 |
. 2
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3 | fvmptd.3 |
. . 3
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4 | fvmptd.2 |
. . . . 5
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5 | 3, 4 | csbied 3010 |
. . . 4
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6 | fvmptd.4 |
. . . 4
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7 | 5, 6 | eqeltrd 2189 |
. . 3
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8 | eqid 2113 |
. . . 4
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9 | 8 | fvmpts 5451 |
. . 3
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10 | 3, 7, 9 | syl2anc 406 |
. 2
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11 | 2, 10, 5 | 3eqtrd 2149 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1404 ax-7 1405 ax-gen 1406 ax-ie1 1450 ax-ie2 1451 ax-8 1463 ax-10 1464 ax-11 1465 ax-i12 1466 ax-bndl 1467 ax-4 1468 ax-14 1473 ax-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-ext 2095 ax-sep 4004 ax-pow 4056 ax-pr 4089 |
This theorem depends on definitions: df-bi 116 df-3an 945 df-tru 1315 df-nf 1418 df-sb 1717 df-eu 1976 df-mo 1977 df-clab 2100 df-cleq 2106 df-clel 2109 df-nfc 2242 df-ral 2393 df-rex 2394 df-v 2657 df-sbc 2877 df-csb 2970 df-un 3039 df-in 3041 df-ss 3048 df-pw 3476 df-sn 3497 df-pr 3498 df-op 3500 df-uni 3701 df-br 3894 df-opab 3948 df-mpt 3949 df-id 4173 df-xp 4503 df-rel 4504 df-cnv 4505 df-co 4506 df-dm 4507 df-iota 5044 df-fun 5081 df-fv 5087 |
This theorem is referenced by: fvmptdv2 5462 rdgivallem 6230 1stinl 6909 2ndinl 6910 1stinr 6911 2ndinr 6912 updjudhcoinlf 6915 updjudhcoinrg 6916 cardcl 6984 caucvgsrlemfv 7527 caucvgsrlemoffval 7532 axcaucvglemval 7626 negiso 8617 infrenegsupex 9285 iseqf1olemfvp 10157 seq3f1olemqsum 10160 infxrnegsupex 10918 climcvg1nlem 11004 isumshft 11145 lmfval 12198 blfvalps 12368 cdivcncfap 12567 peano4nninf 12881 peano3nninf 12882 nninfsellemeq 12891 nninfsellemeqinf 12893 |
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