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Mirrors > Home > ILE Home > Th. List > vscaid | Unicode version |
Description: Utility theorem: index-independent form of scalar product df-vsca 12339. (Contributed by Mario Carneiro, 2-Oct-2013.) (Revised by Mario Carneiro, 19-Jun-2014.) |
Ref | Expression |
---|---|
vscaid | Slot |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-vsca 12339 | . 2 Slot | |
2 | 6nn 9003 | . 2 | |
3 | 1, 2 | ndxid 12284 | 1 Slot |
Colors of variables: wff set class |
Syntax hints: wceq 1335 cfv 5172 c6 8893 cnx 12257 Slot cslot 12259 cvsca 12326 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-13 2130 ax-14 2131 ax-ext 2139 ax-sep 4084 ax-pow 4137 ax-pr 4171 ax-un 4395 ax-cnex 7825 ax-resscn 7826 ax-1re 7828 ax-addrcl 7831 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-sbc 2938 df-un 3106 df-in 3108 df-ss 3115 df-pw 3546 df-sn 3567 df-pr 3568 df-op 3570 df-uni 3775 df-int 3810 df-br 3968 df-opab 4028 df-mpt 4029 df-id 4255 df-xp 4594 df-rel 4595 df-cnv 4596 df-co 4597 df-dm 4598 df-rn 4599 df-res 4600 df-iota 5137 df-fun 5174 df-fv 5180 df-ov 5829 df-inn 8839 df-2 8897 df-3 8898 df-4 8899 df-5 8900 df-6 8901 df-ndx 12263 df-slot 12264 df-vsca 12339 |
This theorem is referenced by: (None) |
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