Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > fvmptt | Unicode version |
Description: Closed theorem form of fvmpt 5585. (Contributed by Scott Fenton, 21-Feb-2013.) (Revised by Mario Carneiro, 11-Sep-2015.) |
Ref | Expression |
---|---|
fvmptt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp2 998 | . . 3 | |
2 | 1 | fveq1d 5509 | . 2 |
3 | risset 2503 | . . . . 5 | |
4 | elex 2746 | . . . . . 6 | |
5 | nfa1 1539 | . . . . . . 7 | |
6 | nfv 1526 | . . . . . . . 8 | |
7 | nffvmpt1 5518 | . . . . . . . . 9 | |
8 | 7 | nfeq1 2327 | . . . . . . . 8 |
9 | 6, 8 | nfim 1570 | . . . . . . 7 |
10 | simprl 529 | . . . . . . . . . . . . 13 | |
11 | simplr 528 | . . . . . . . . . . . . . 14 | |
12 | simprr 531 | . . . . . . . . . . . . . 14 | |
13 | 11, 12 | eqeltrd 2252 | . . . . . . . . . . . . 13 |
14 | eqid 2175 | . . . . . . . . . . . . . 14 | |
15 | 14 | fvmpt2 5591 | . . . . . . . . . . . . 13 |
16 | 10, 13, 15 | syl2anc 411 | . . . . . . . . . . . 12 |
17 | simpll 527 | . . . . . . . . . . . . 13 | |
18 | 17 | fveq2d 5511 | . . . . . . . . . . . 12 |
19 | 16, 18, 11 | 3eqtr3d 2216 | . . . . . . . . . . 11 |
20 | 19 | exp43 372 | . . . . . . . . . 10 |
21 | 20 | a2i 11 | . . . . . . . . 9 |
22 | 21 | com23 78 | . . . . . . . 8 |
23 | 22 | sps 1535 | . . . . . . 7 |
24 | 5, 9, 23 | rexlimd 2589 | . . . . . 6 |
25 | 4, 24 | syl7 69 | . . . . 5 |
26 | 3, 25 | biimtrid 152 | . . . 4 |
27 | 26 | imp32 257 | . . 3 |
28 | 27 | 3adant2 1016 | . 2 |
29 | 2, 28 | eqtrd 2208 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 104 w3a 978 wal 1351 wceq 1353 wcel 2146 wrex 2454 cvv 2735 cmpt 4059 cfv 5208 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1445 ax-7 1446 ax-gen 1447 ax-ie1 1491 ax-ie2 1492 ax-8 1502 ax-10 1503 ax-11 1504 ax-i12 1505 ax-bndl 1507 ax-4 1508 ax-17 1524 ax-i9 1528 ax-ial 1532 ax-i5r 1533 ax-14 2149 ax-ext 2157 ax-sep 4116 ax-pow 4169 ax-pr 4203 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1459 df-sb 1761 df-eu 2027 df-mo 2028 df-clab 2162 df-cleq 2168 df-clel 2171 df-nfc 2306 df-ral 2458 df-rex 2459 df-v 2737 df-sbc 2961 df-csb 3056 df-un 3131 df-in 3133 df-ss 3140 df-pw 3574 df-sn 3595 df-pr 3596 df-op 3598 df-uni 3806 df-br 3999 df-opab 4060 df-mpt 4061 df-id 4287 df-xp 4626 df-rel 4627 df-cnv 4628 df-co 4629 df-dm 4630 df-iota 5170 df-fun 5210 df-fv 5216 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |