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Theorem suppssfvOLD 6531
 Description: Formula building theorem for support restriction, on a function which preserves zero. (Contributed by Stefan O'Rear, 9-Mar-2015.) Obsolete version of suppssfv 6955 as of 28-May-2019. (New usage is discouraged.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
suppssfvOLD.a
suppssfvOLD.f
suppssfvOLD.v
Assertion
Ref Expression
suppssfvOLD
Distinct variable groups:   ,   ,   ,

Proof of Theorem suppssfvOLD
StepHypRef Expression
1 eldifsni 4156 . . . . 5
2 suppssfvOLD.v . . . . . . . . 9
3 elex 3118 . . . . . . . . 9
42, 3syl 16 . . . . . . . 8
54adantr 465 . . . . . . 7
6 suppssfvOLD.f . . . . . . . . . . 11
7 fveq2 5871 . . . . . . . . . . . 12
87eqeq1d 2459 . . . . . . . . . . 11
96, 8syl5ibrcom 222 . . . . . . . . . 10
109necon3d 2681 . . . . . . . . 9
1110adantr 465 . . . . . . . 8
1211imp 429 . . . . . . 7
13 eldifsn 4155 . . . . . . 7
145, 12, 13sylanbrc 664 . . . . . 6
1514ex 434 . . . . 5
161, 15syl5 32 . . . 4
1716ss2rabdv 3580 . . 3
18 eqid 2457 . . . 4
1918mptpreima 5505 . . 3
20 eqid 2457 . . . 4
2120mptpreima 5505 . . 3
2217, 19, 213sstr4g 3544 . 2
23 suppssfvOLD.a . 2
2422, 23sstrd 3513 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  e.wcel 1818  =/=wne 2652  {crab 2811   cvv 3109  \cdif 3472  C_wss 3475  {csn 4029  e.cmpt 4510  'ccnv 5003  "cima 5007  cfv 5593 This theorem is referenced by:  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
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