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Mirrors > Home > ILE Home > Th. List > fvmptdf | Unicode version |
Description: Alternate deduction version of fvmpt 5491, suitable for iteration. (Contributed by Mario Carneiro, 7-Jan-2017.) |
Ref | Expression |
---|---|
fvmptdf.1 | |
fvmptdf.2 | |
fvmptdf.3 | |
fvmptdf.4 | |
fvmptdf.5 |
Ref | Expression |
---|---|
fvmptdf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1508 | . 2 | |
2 | fvmptdf.4 | . . . 4 | |
3 | nfmpt1 4016 | . . . 4 | |
4 | 2, 3 | nfeq 2287 | . . 3 |
5 | fvmptdf.5 | . . 3 | |
6 | 4, 5 | nfim 1551 | . 2 |
7 | fvmptdf.1 | . . . 4 | |
8 | elex 2692 | . . . 4 | |
9 | 7, 8 | syl 14 | . . 3 |
10 | isset 2687 | . . 3 | |
11 | 9, 10 | sylib 121 | . 2 |
12 | fveq1 5413 | . . 3 | |
13 | simpr 109 | . . . . . . 7 | |
14 | 13 | fveq2d 5418 | . . . . . 6 |
15 | 7 | adantr 274 | . . . . . . . 8 |
16 | 13, 15 | eqeltrd 2214 | . . . . . . 7 |
17 | fvmptdf.2 | . . . . . . 7 | |
18 | eqid 2137 | . . . . . . . 8 | |
19 | 18 | fvmpt2 5497 | . . . . . . 7 |
20 | 16, 17, 19 | syl2anc 408 | . . . . . 6 |
21 | 14, 20 | eqtr3d 2172 | . . . . 5 |
22 | 21 | eqeq2d 2149 | . . . 4 |
23 | fvmptdf.3 | . . . 4 | |
24 | 22, 23 | sylbid 149 | . . 3 |
25 | 12, 24 | syl5 32 | . 2 |
26 | 1, 6, 11, 25 | exlimdd 1844 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1331 wnf 1436 wex 1468 wcel 1480 wnfc 2266 cvv 2681 cmpt 3984 cfv 5118 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-sbc 2905 df-csb 2999 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-opab 3985 df-mpt 3986 df-id 4210 df-xp 4540 df-rel 4541 df-cnv 4542 df-co 4543 df-dm 4544 df-iota 5083 df-fun 5120 df-fv 5126 |
This theorem is referenced by: fvmptdv 5502 |
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