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Mirrors > Home > MPE Home > Th. List > scaid | Structured version Visualization version GIF version |
Description: Utility theorem: index-independent form of scalar df-sca 17148. (Contributed by Mario Carneiro, 19-Jun-2014.) |
Ref | Expression |
---|---|
scaid | ⊢ Scalar = Slot (Scalar‘ndx) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-sca 17148 | . 2 ⊢ Scalar = Slot 5 | |
2 | 5nn 12238 | . 2 ⊢ 5 ∈ ℕ | |
3 | 1, 2 | ndxid 17068 | 1 ⊢ Scalar = Slot (Scalar‘ndx) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1541 ‘cfv 6496 5c5 12210 Slot cslot 17052 ndxcnx 17064 Scalarcsca 17135 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-10 2137 ax-11 2154 ax-12 2171 ax-ext 2707 ax-sep 5256 ax-nul 5263 ax-pow 5320 ax-pr 5384 ax-un 7671 ax-cnex 11106 ax-1cn 11108 ax-addcl 11110 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 846 df-3or 1088 df-3an 1089 df-tru 1544 df-fal 1554 df-ex 1782 df-nf 1786 df-sb 2068 df-mo 2538 df-eu 2567 df-clab 2714 df-cleq 2728 df-clel 2814 df-nfc 2889 df-ne 2944 df-ral 3065 df-rex 3074 df-reu 3354 df-rab 3408 df-v 3447 df-sbc 3740 df-csb 3856 df-dif 3913 df-un 3915 df-in 3917 df-ss 3927 df-pss 3929 df-nul 4283 df-if 4487 df-pw 4562 df-sn 4587 df-pr 4589 df-op 4593 df-uni 4866 df-iun 4956 df-br 5106 df-opab 5168 df-mpt 5189 df-tr 5223 df-id 5531 df-eprel 5537 df-po 5545 df-so 5546 df-fr 5588 df-we 5590 df-xp 5639 df-rel 5640 df-cnv 5641 df-co 5642 df-dm 5643 df-rn 5644 df-res 5645 df-ima 5646 df-pred 6253 df-ord 6320 df-on 6321 df-lim 6322 df-suc 6323 df-iota 6448 df-fun 6498 df-fn 6499 df-f 6500 df-f1 6501 df-fo 6502 df-f1o 6503 df-fv 6504 df-ov 7359 df-om 7802 df-2nd 7921 df-frecs 8211 df-wrecs 8242 df-recs 8316 df-rdg 8355 df-nn 12153 df-2 12215 df-3 12216 df-4 12217 df-5 12218 df-slot 17053 df-ndx 17065 df-sca 17148 |
This theorem is referenced by: lmodsca 17208 ipssca 17220 resssca 17223 phlsca 17229 prdssca 17337 imassca 17400 mgpsca 19902 rmodislmod 20388 rmodislmodOLD 20389 srasca 20644 srascaOLD 20645 zlmsca 20923 psrsca 21355 opsrsca 21458 psr1sca2 21620 ply1sca2 21623 matsca 21760 matscaOLD 21761 tngsca 24003 resvsca 32065 bj-isrvec 35755 algsca 41485 mendsca 41493 mnringscad 42483 |
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