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Mirrors > Home > ILE Home > Th. List > fvmptdf | Unicode version |
Description: Alternate deduction version of fvmpt 5571, 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 1521 | . 2 | |
2 | fvmptdf.4 | . . . 4 | |
3 | nfmpt1 4080 | . . . 4 | |
4 | 2, 3 | nfeq 2320 | . . 3 |
5 | fvmptdf.5 | . . 3 | |
6 | 4, 5 | nfim 1565 | . 2 |
7 | fvmptdf.1 | . . . 4 | |
8 | elex 2741 | . . . 4 | |
9 | 7, 8 | syl 14 | . . 3 |
10 | isset 2736 | . . 3 | |
11 | 9, 10 | sylib 121 | . 2 |
12 | fveq1 5493 | . . 3 | |
13 | simpr 109 | . . . . . . 7 | |
14 | 13 | fveq2d 5498 | . . . . . 6 |
15 | 7 | adantr 274 | . . . . . . . 8 |
16 | 13, 15 | eqeltrd 2247 | . . . . . . 7 |
17 | fvmptdf.2 | . . . . . . 7 | |
18 | eqid 2170 | . . . . . . . 8 | |
19 | 18 | fvmpt2 5577 | . . . . . . 7 |
20 | 16, 17, 19 | syl2anc 409 | . . . . . 6 |
21 | 14, 20 | eqtr3d 2205 | . . . . 5 |
22 | 21 | eqeq2d 2182 | . . . 4 |
23 | fvmptdf.3 | . . . 4 | |
24 | 22, 23 | sylbid 149 | . . 3 |
25 | 12, 24 | syl5 32 | . 2 |
26 | 1, 6, 11, 25 | exlimdd 1865 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1348 wnf 1453 wex 1485 wcel 2141 wnfc 2299 cvv 2730 cmpt 4048 cfv 5196 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4105 ax-pow 4158 ax-pr 4192 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-sbc 2956 df-csb 3050 df-un 3125 df-in 3127 df-ss 3134 df-pw 3566 df-sn 3587 df-pr 3588 df-op 3590 df-uni 3795 df-br 3988 df-opab 4049 df-mpt 4050 df-id 4276 df-xp 4615 df-rel 4616 df-cnv 4617 df-co 4618 df-dm 4619 df-iota 5158 df-fun 5198 df-fv 5204 |
This theorem is referenced by: fvmptdv 5582 |
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