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Theorem suppssof1OLD 6559
Description: Formula building theorem for support restrictions: vector operation with left annihilator. (Contributed by Stefan O'Rear, 9-Mar-2015.) Obsolete version of suppssof1 6952 as of 28-May-2019. (New usage is discouraged.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
suppssof1OLD.s
suppssof1OLD.o
suppssof1OLD.a
suppssof1OLD.b
suppssof1OLD.d
Assertion
Ref Expression
suppssof1OLD
Distinct variable groups:   ,   ,   ,O   ,   ,   ,

Proof of Theorem suppssof1OLD
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 suppssof1OLD.a . . . . . 6
2 ffn 5736 . . . . . 6
31, 2syl 16 . . . . 5
4 suppssof1OLD.b . . . . . 6
5 ffn 5736 . . . . . 6
64, 5syl 16 . . . . 5
7 suppssof1OLD.d . . . . 5
8 inidm 3706 . . . . 5
9 eqidd 2458 . . . . 5
10 eqidd 2458 . . . . 5
113, 6, 7, 7, 8, 9, 10offval 6547 . . . 4
1211cnveqd 5183 . . 3
1312imaeq1d 5341 . 2
141feqmptd 5926 . . . . . 6
1514cnveqd 5183 . . . . 5
1615imaeq1d 5341 . . . 4
17 suppssof1OLD.s . . . 4
1816, 17eqsstr3d 3538 . . 3
19 suppssof1OLD.o . . 3
20 fvex 5881 . . . 4
2120a1i 11 . . 3
224ffvelrnda 6031 . . 3
2318, 19, 21, 22suppssov1OLD 6532 . 2
2413, 23eqsstrd 3537 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  e.wcel 1818   cvv 3109  \cdif 3472  C_wss 3475  {csn 4029  e.cmpt 4510  `'ccnv 5003  "cima 5007  Fnwfn 5588  -->wf 5589  `cfv 5593  (class class class)co 6296  oFcof 6538
This theorem is referenced by:  psrbagev1OLD  18178
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-rep 4563  ax-sep 4573  ax-nul 4581  ax-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-reu 2814  df-rab 2816  df-v 3111  df-sbc 3328  df-csb 3435  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-iun 4332  df-br 4453  df-opab 4511  df-mpt 4512  df-id 4800  df-xp 5010  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-rn 5015  df-res 5016  df-ima 5017  df-iota 5556  df-fun 5595  df-fn 5596  df-f 5597  df-f1 5598  df-fo 5599  df-f1o 5600  df-fv 5601  df-ov 6299  df-oprab 6300  df-mpt2 6301  df-of 6540
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