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Mirrors > Home > ILE Home > Th. List > fvmptd | Unicode version |
Description: Deduction version of fvmpt 5381. (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 5307 |
. 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 2974 |
. . . 4
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6 | fvmptd.4 |
. . . 4
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7 | 5, 6 | eqeltrd 2164 |
. . 3
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8 | eqid 2088 |
. . . 4
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9 | 8 | fvmpts 5382 |
. . 3
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10 | 3, 7, 9 | syl2anc 403 |
. 2
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11 | 2, 10, 5 | 3eqtrd 2124 |
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: fvmptdv2 5392 rdgivallem 6146 djuss 6759 1stinl 6763 2ndinl 6764 1stinr 6765 2ndinr 6766 updjudhcoinlf 6769 updjudhcoinrg 6770 cardcl 6807 caucvgsrlemfv 7334 caucvgsrlemoffval 7339 axcaucvglemval 7430 negiso 8414 infrenegsupex 9080 iseqf1olemfvp 9922 seq3f1olemqsum 9925 climcvg1nlem 10734 isumshft 10880 peano4nninf 11851 peano3nninf 11852 nninfsellemeq 11861 nninfsellemeqinf 11863 |
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