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Theorem caovcl 6469
Description: Convert an operation closure law to class notation. (Contributed by NM, 4-Aug-1995.) (Revised by Mario Carneiro, 26-May-2014.)
Hypothesis
Ref Expression
caovcl.1
Assertion
Ref Expression
caovcl
Distinct variable groups:   , ,   ,   , ,   ,S,

Proof of Theorem caovcl
StepHypRef Expression
1 tru 1399 . 2
2 caovcl.1 . . . 4
32adantl 466 . . 3
43caovclg 6467 . 2
51, 4mpan 670 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369   wtru 1396  e.wcel 1818  (class class class)co 6296
This theorem is referenced by:  ecopovtrn  7433  eceqoveq  7435  genpss  9403  genpnnp  9404  genpass  9408  expcllem  12177  txlly  20137  txnlly  20138
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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
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-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  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-iota 5556  df-fv 5601  df-ov 6299
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