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Mirrors > Home > ILE Home > Th. List > fvmptt | Unicode version |
Description: Closed theorem form of fvmpt 5249. (Contributed by Scott Fenton, 21-Feb-2013.) (Revised by Mario Carneiro, 11-Sep-2015.) |
Ref | Expression |
---|---|
fvmptt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp2 905 | . . 3 | |
2 | 1 | fveq1d 5180 | . 2 |
3 | risset 2352 | . . . . 5 | |
4 | elex 2566 | . . . . . 6 | |
5 | nfa1 1434 | . . . . . . 7 | |
6 | nfv 1421 | . . . . . . . 8 | |
7 | nffvmpt1 5186 | . . . . . . . . 9 | |
8 | 7 | nfeq1 2187 | . . . . . . . 8 |
9 | 6, 8 | nfim 1464 | . . . . . . 7 |
10 | simprl 483 | . . . . . . . . . . . . 13 | |
11 | simplr 482 | . . . . . . . . . . . . . 14 | |
12 | simprr 484 | . . . . . . . . . . . . . 14 | |
13 | 11, 12 | eqeltrd 2114 | . . . . . . . . . . . . 13 |
14 | eqid 2040 | . . . . . . . . . . . . . 14 | |
15 | 14 | fvmpt2 5254 | . . . . . . . . . . . . 13 |
16 | 10, 13, 15 | syl2anc 391 | . . . . . . . . . . . 12 |
17 | simpll 481 | . . . . . . . . . . . . 13 | |
18 | 17 | fveq2d 5182 | . . . . . . . . . . . 12 |
19 | 16, 18, 11 | 3eqtr3d 2080 | . . . . . . . . . . 11 |
20 | 19 | exp43 354 | . . . . . . . . . 10 |
21 | 20 | a2i 11 | . . . . . . . . 9 |
22 | 21 | com23 72 | . . . . . . . 8 |
23 | 22 | sps 1430 | . . . . . . 7 |
24 | 5, 9, 23 | rexlimd 2430 | . . . . . 6 |
25 | 4, 24 | syl7 63 | . . . . 5 |
26 | 3, 25 | syl5bi 141 | . . . 4 |
27 | 26 | imp32 244 | . . 3 |
28 | 27 | 3adant2 923 | . 2 |
29 | 2, 28 | eqtrd 2072 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 w3a 885 wal 1241 wceq 1243 wcel 1393 wrex 2307 cvv 2557 cmpt 3818 cfv 4902 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-sbc 2765 df-csb 2853 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-br 3765 df-opab 3819 df-mpt 3820 df-id 4030 df-xp 4351 df-rel 4352 df-cnv 4353 df-co 4354 df-dm 4355 df-iota 4867 df-fun 4904 df-fv 4910 |
This theorem is referenced by: (None) |
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