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Theorem ovmpt2g 6210
 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:   ,,   ,,   ,,   ,,   ,,
Allowed substitution hints:   (,)   (,)   (,)   (,)

Proof of Theorem ovmpt2g
StepHypRef Expression
1 ovmpt2g.1 . . 3
2 ovmpt2g.2 . . 3
31, 2sylan9eq 2490 . 2
4 ovmpt2g.3 . 2
53, 4ovmpt2ga 6205 1
 Colors of variables: wff set class Syntax hints:   wi 4   w3a 937   wceq 1653   wcel 1726  (class class class)co 6083   cmpt2 6085 This theorem is referenced by:  ovmpt2  6211  mapvalg  7030  pmvalg  7031  cdaval  8052  genpv  8878  shftfval  11887  symgov  15102  bcthlem1  19279  elghomlem1  21951  mendmulr  27475  paddval  30657  tgrpov  31607  erngmul  31665  erngmul-rN  31673  dvamulr  31871  dvavadd  31874  dvhmulr  31946  djavalN  31995  djhval  32258 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-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-rab 2716  df-v 2960  df-sbc 3164  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-br 4215  df-opab 4269  df-id 4500  df-xp 4886  df-rel 4887  df-cnv 4888  df-co 4889  df-dm 4890  df-iota 5420  df-fun 5458  df-fv 5464  df-ov 6086  df-oprab 6087  df-mpt2 6088
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