![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > vscaid | Unicode version |
Description: Utility theorem: index-independent form of scalar product df-vsca 11875. (Contributed by Mario Carneiro, 2-Oct-2013.) (Revised by Mario Carneiro, 19-Jun-2014.) |
Ref | Expression |
---|---|
vscaid |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-vsca 11875 |
. 2
![]() ![]() ![]() ![]() | |
2 | 6nn 8783 |
. 2
![]() ![]() ![]() ![]() | |
3 | 1, 2 | ndxid 11820 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1404 ax-7 1405 ax-gen 1406 ax-ie1 1450 ax-ie2 1451 ax-8 1463 ax-10 1464 ax-11 1465 ax-i12 1466 ax-bndl 1467 ax-4 1468 ax-13 1472 ax-14 1473 ax-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-ext 2095 ax-sep 4004 ax-pow 4056 ax-pr 4089 ax-un 4313 ax-cnex 7630 ax-resscn 7631 ax-1re 7633 ax-addrcl 7636 |
This theorem depends on definitions: df-bi 116 df-3an 945 df-tru 1315 df-nf 1418 df-sb 1717 df-eu 1976 df-mo 1977 df-clab 2100 df-cleq 2106 df-clel 2109 df-nfc 2242 df-ral 2393 df-rex 2394 df-v 2657 df-sbc 2877 df-un 3039 df-in 3041 df-ss 3048 df-pw 3476 df-sn 3497 df-pr 3498 df-op 3500 df-uni 3701 df-int 3736 df-br 3894 df-opab 3948 df-mpt 3949 df-id 4173 df-xp 4503 df-rel 4504 df-cnv 4505 df-co 4506 df-dm 4507 df-rn 4508 df-res 4509 df-iota 5044 df-fun 5081 df-fv 5087 df-ov 5729 df-inn 8625 df-2 8683 df-3 8684 df-4 8685 df-5 8686 df-6 8687 df-ndx 11799 df-slot 11800 df-vsca 11875 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |