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Theorem suppssof1 6833
 Description: Formula building theorem for support restrictions: vector operation with left annihilator. (Contributed by Stefan O'Rear, 9-Mar-2015.) (Revised by AV, 28-May-2019.)
Hypotheses
Ref Expression
suppssof1.s supp
suppssof1.o
suppssof1.a
suppssof1.b
suppssof1.d
suppssof1.y
Assertion
Ref Expression
suppssof1 supp
Distinct variable groups:   ,   ,   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()   ()   ()   ()

Proof of Theorem suppssof1
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 suppssof1.a . . . . 5
2 ffn 5668 . . . . 5
31, 2syl 16 . . . 4
4 suppssof1.b . . . . 5
5 ffn 5668 . . . . 5
64, 5syl 16 . . . 4
7 suppssof1.d . . . 4
8 inidm 3668 . . . 4
9 eqidd 2455 . . . 4
10 eqidd 2455 . . . 4
113, 6, 7, 7, 8, 9, 10offval 6438 . . 3
1211oveq1d 6216 . 2 supp supp
131feqmptd 5854 . . . . 5
1413oveq1d 6216 . . . 4 supp supp
15 suppssof1.s . . . 4 supp
1614, 15eqsstr3d 3500 . . 3 supp
17 suppssof1.o . . 3
18 fvex 5810 . . . 4
1918a1i 11 . . 3
204ffvelrnda 5953 . . 3
21 suppssof1.y . . 3
2216, 17, 19, 20, 21suppssov1 6832 . 2 supp
2312, 22eqsstrd 3499 1 supp
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   wceq 1370   wcel 1758  cvv 3078   wss 3437   cmpt 4459   wfn 5522  wf 5523  cfv 5527  (class class class)co 6201   cof 6429   supp csupp 6801 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-8 1760  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432  ax-rep 4512  ax-sep 4522  ax-nul 4530  ax-pow 4579  ax-pr 4640  ax-un 6483 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-eu 2266  df-mo 2267  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2650  df-ral 2804  df-rex 2805  df-reu 2806  df-rab 2808  df-v 3080  df-sbc 3295  df-csb 3397  df-dif 3440  df-un 3442  df-in 3444  df-ss 3451  df-nul 3747  df-if 3901  df-sn 3987  df-pr 3989  df-op 3993  df-uni 4201  df-iun 4282  df-br 4402  df-opab 4460  df-mpt 4461  df-id 4745  df-xp 4955  df-rel 4956  df-cnv 4957  df-co 4958  df-dm 4959  df-rn 4960  df-res 4961  df-ima 4962  df-iota 5490  df-fun 5529  df-fn 5530  df-f 5531  df-f1 5532  df-fo 5533  df-f1o 5534  df-fv 5535  df-ov 6204  df-oprab 6205  df-mpt2 6206  df-of 6431  df-supp 6802 This theorem is referenced by:  psrbagev1  17719  frlmup1  18352  jensen  22516
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