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Theorem ovmpt2g 6437
Description: Value of an operation given by a maps-to rule. Special case. (Contributed by NM, 14-Sep-1999.) (Revised by David Abernethy, 19-Jun-2012.)
Hypotheses
Ref Expression
ovmpt2g.1
ovmpt2g.2
ovmpt2g.3
Assertion
Ref Expression
ovmpt2g
Distinct variable groups:   , ,   , ,   , ,   , ,   ,S,

Proof of Theorem ovmpt2g
StepHypRef Expression
1 ovmpt2g.1 . . 3
2 ovmpt2g.2 . . 3
31, 2sylan9eq 2518 . 2
4 ovmpt2g.3 . 2
53, 4ovmpt2ga 6432 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\w3a 973  =wceq 1395  e.wcel 1818  (class class class)co 6296  e.cmpt2 6298
This theorem is referenced by:  ovmpt2  6438  mapvalg  7449  pmvalg  7450  cdaval  8571  genpv  9398  shftfval  12903  symgov  16415  frlmipval  18810  bcthlem1  21763  motplusg  23929  elghomlem1OLD  25363  signspval  28509  mendmulr  31137  paddval  35522  tgrpov  36474  erngmul  36532  erngmul-rN  36540  dvamulr  36738  dvavadd  36741  dvhmulr  36813  djavalN  36862  djhval  37125
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-sbc 3328  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-id 4800  df-xp 5010  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-iota 5556  df-fun 5595  df-fv 5601  df-ov 6299  df-oprab 6300  df-mpt2 6301
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