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Theorem suppssov1OLD 6532
Description: Formula building theorem for support restrictions: operator with left annihilator. (Contributed by Stefan O'Rear, 9-Mar-2015.) Obsolete version of suppssov1 6951 as of 28-May-2019. (New usage is discouraged.)
Hypotheses
Ref Expression
suppssov1OLD.s
suppssov1OLD.o
suppssov1OLD.a
suppssov1OLD.b
Assertion
Ref Expression
suppssov1OLD
Distinct variable groups:   ,   ,   ,   ,O   ,   ,   ,   ,   ,

Proof of Theorem suppssov1OLD
StepHypRef Expression
1 suppssov1OLD.a . . . . . . . 8
2 elex 3118 . . . . . . . 8
31, 2syl 16 . . . . . . 7
43adantr 465 . . . . . 6
5 eldifsni 4156 . . . . . . . 8
6 suppssov1OLD.b . . . . . . . . . . 11
7 suppssov1OLD.o . . . . . . . . . . . . 13
87ralrimiva 2871 . . . . . . . . . . . 12
98adantr 465 . . . . . . . . . . 11
10 oveq2 6304 . . . . . . . . . . . . 13
1110eqeq1d 2459 . . . . . . . . . . . 12
1211rspcva 3208 . . . . . . . . . . 11
136, 9, 12syl2anc 661 . . . . . . . . . 10
14 oveq1 6303 . . . . . . . . . . 11
1514eqeq1d 2459 . . . . . . . . . 10
1613, 15syl5ibrcom 222 . . . . . . . . 9
1716necon3d 2681 . . . . . . . 8
185, 17syl5 32 . . . . . . 7
1918imp 429 . . . . . 6
20 eldifsn 4155 . . . . . 6
214, 19, 20sylanbrc 664 . . . . 5
2221ex 434 . . . 4
2322ss2rabdv 3580 . . 3
24 eqid 2457 . . . 4
2524mptpreima 5505 . . 3
26 eqid 2457 . . . 4
2726mptpreima 5505 . . 3
2823, 25, 273sstr4g 3544 . 2
29 suppssov1OLD.s . 2
3028, 29sstrd 3513 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  e.wcel 1818  =/=wne 2652  A.wral 2807  {crab 2811   cvv 3109  \cdif 3472  C_wss 3475  {csn 4029  e.cmpt 4510  `'ccnv 5003  "cima 5007  (class class class)co 6296
This theorem is referenced by:  suppssof1OLD  6559  evlslem6OLD  18182
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-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-rab 2816  df-v 3111  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-br 4453  df-opab 4511  df-mpt 4512  df-xp 5010  df-rel 5011  df-cnv 5012  df-dm 5014  df-rn 5015  df-res 5016  df-ima 5017  df-iota 5556  df-fv 5601  df-ov 6299
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