Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > fvmptt | Unicode version |
Description: Closed theorem form of fvmpt 5270. (Contributed by Scott Fenton, 21-Feb-2013.) (Revised by Mario Carneiro, 11-Sep-2015.) |
Ref | Expression |
---|---|
fvmptt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp2 939 | . . 3 | |
2 | 1 | fveq1d 5200 | . 2 |
3 | risset 2394 | . . . . 5 | |
4 | elex 2610 | . . . . . 6 | |
5 | nfa1 1474 | . . . . . . 7 | |
6 | nfv 1461 | . . . . . . . 8 | |
7 | nffvmpt1 5206 | . . . . . . . . 9 | |
8 | 7 | nfeq1 2228 | . . . . . . . 8 |
9 | 6, 8 | nfim 1504 | . . . . . . 7 |
10 | simprl 497 | . . . . . . . . . . . . 13 | |
11 | simplr 496 | . . . . . . . . . . . . . 14 | |
12 | simprr 498 | . . . . . . . . . . . . . 14 | |
13 | 11, 12 | eqeltrd 2155 | . . . . . . . . . . . . 13 |
14 | eqid 2081 | . . . . . . . . . . . . . 14 | |
15 | 14 | fvmpt2 5275 | . . . . . . . . . . . . 13 |
16 | 10, 13, 15 | syl2anc 403 | . . . . . . . . . . . 12 |
17 | simpll 495 | . . . . . . . . . . . . 13 | |
18 | 17 | fveq2d 5202 | . . . . . . . . . . . 12 |
19 | 16, 18, 11 | 3eqtr3d 2121 | . . . . . . . . . . 11 |
20 | 19 | exp43 364 | . . . . . . . . . 10 |
21 | 20 | a2i 11 | . . . . . . . . 9 |
22 | 21 | com23 77 | . . . . . . . 8 |
23 | 22 | sps 1470 | . . . . . . 7 |
24 | 5, 9, 23 | rexlimd 2474 | . . . . . 6 |
25 | 4, 24 | syl7 68 | . . . . 5 |
26 | 3, 25 | syl5bi 150 | . . . 4 |
27 | 26 | imp32 253 | . . 3 |
28 | 27 | 3adant2 957 | . 2 |
29 | 2, 28 | eqtrd 2113 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 w3a 919 wal 1282 wceq 1284 wcel 1433 wrex 2349 cvv 2601 cmpt 3839 cfv 4922 |
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 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-v 2603 df-sbc 2816 df-csb 2909 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-br 3786 df-opab 3840 df-mpt 3841 df-id 4048 df-xp 4369 df-rel 4370 df-cnv 4371 df-co 4372 df-dm 4373 df-iota 4887 df-fun 4924 df-fv 4930 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |