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Theorem suppssof1 6348
 Description: Formula building theorem for support restrictions: vector operation with left annihilator. (Contributed by Stefan O'Rear, 9-Mar-2015.)
Hypotheses
Ref Expression
suppssof1.s
suppssof1.o
suppssof1.a
suppssof1.b
suppssof1.d
Assertion
Ref Expression
suppssof1
Distinct variable groups:   ,   ,   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()   ()   ()

Proof of Theorem suppssof1
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 suppssof1.a . . . . . 6
2 ffn 5593 . . . . . 6
31, 2syl 16 . . . . 5
4 suppssof1.b . . . . . 6
5 ffn 5593 . . . . . 6
64, 5syl 16 . . . . 5
7 suppssof1.d . . . . 5
8 inidm 3552 . . . . 5
9 eqidd 2439 . . . . 5
10 eqidd 2439 . . . . 5
113, 6, 7, 7, 8, 9, 10offval 6314 . . . 4
1211cnveqd 5050 . . 3
1312imaeq1d 5204 . 2
141feqmptd 5781 . . . . . 6
1514cnveqd 5050 . . . . 5
1615imaeq1d 5204 . . . 4
17 suppssof1.s . . . 4
1816, 17eqsstr3d 3385 . . 3
19 suppssof1.o . . 3
20 fvex 5744 . . . 4
2120a1i 11 . . 3
224ffvelrnda 5872 . . 3
2318, 19, 21, 22suppssov1 6304 . 2
2413, 23eqsstrd 3384 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wceq 1653   wcel 1726  cvv 2958   cdif 3319   wss 3322  csn 3816   cmpt 4268  ccnv 4879  cima 4883   wfn 5451  wf 5452  cfv 5456  (class class class)co 6083   cof 6305 This theorem is referenced by:  psrbagev1  16568  jensen  20829 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-rep 4322  ax-sep 4332  ax-nul 4340  ax-pr 4405 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-reu 2714  df-rab 2716  df-v 2960  df-sbc 3164  df-csb 3254  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-iun 4097  df-br 4215  df-opab 4269  df-mpt 4270  df-id 4500  df-xp 4886  df-rel 4887  df-cnv 4888  df-co 4889  df-dm 4890  df-rn 4891  df-res 4892  df-ima 4893  df-iota 5420  df-fun 5458  df-fn 5459  df-f 5460  df-f1 5461  df-fo 5462  df-f1o 5463  df-fv 5464  df-ov 6086  df-oprab 6087  df-mpt2 6088  df-of 6307
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