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Mirrors > Home > ILE Home > Th. List > fvmptd | Unicode version |
Description: Deduction version of fvmpt 5557. (Contributed by Scott Fenton, 18-Feb-2013.) (Revised by Mario Carneiro, 31-Aug-2015.) |
Ref | Expression |
---|---|
fvmptd.1 | |
fvmptd.2 | |
fvmptd.3 | |
fvmptd.4 |
Ref | Expression |
---|---|
fvmptd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fvmptd.1 | . . 3 | |
2 | 1 | fveq1d 5482 | . 2 |
3 | fvmptd.3 | . . 3 | |
4 | fvmptd.2 | . . . . 5 | |
5 | 3, 4 | csbied 3086 | . . . 4 |
6 | fvmptd.4 | . . . 4 | |
7 | 5, 6 | eqeltrd 2241 | . . 3 |
8 | eqid 2164 | . . . 4 | |
9 | 8 | fvmpts 5558 | . . 3 |
10 | 3, 7, 9 | syl2anc 409 | . 2 |
11 | 2, 10, 5 | 3eqtrd 2201 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1342 wcel 2135 csb 3040 cmpt 4037 cfv 5182 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-sbc 2947 df-csb 3041 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-br 3977 df-opab 4038 df-mpt 4039 df-id 4265 df-xp 4604 df-rel 4605 df-cnv 4606 df-co 4607 df-dm 4608 df-iota 5147 df-fun 5184 df-fv 5190 |
This theorem is referenced by: fvmptdv2 5569 rdgivallem 6340 1stinl 7030 2ndinl 7031 1stinr 7032 2ndinr 7033 updjudhcoinlf 7036 updjudhcoinrg 7037 cardcl 7128 caucvgsrlemfv 7723 caucvgsrlemoffval 7728 axcaucvglemval 7829 negiso 8841 infrenegsupex 9523 iseqf1olemfvp 10422 seq3f1olemqsum 10425 infxrnegsupex 11190 climcvg1nlem 11276 isumshft 11417 lmfval 12739 blfvalps 12932 cdivcncfap 13134 peano4nninf 13727 peano3nninf 13728 nninfsellemeq 13735 nninfsellemeqinf 13737 |
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