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Theorem caovcl 6244
 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:   ,,   ,   ,,   ,,
Allowed substitution hint:   ()

Proof of Theorem caovcl
StepHypRef Expression
1 tru 1331 . 2
2 caovcl.1 . . . 4
32adantl 454 . . 3
43caovclg 6242 . 2
51, 4mpan 653 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wtru 1326   wcel 1726  (class class class)co 6084 This theorem is referenced by:  ecopovtrn  7010  eceqoveq  7012  genpss  8886  genpnnp  8887  genpass  8891  expcllem  11397  txlly  17673  txnlly  17674 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 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-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  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 4216  df-iota 5421  df-fv 5465  df-ov 6087
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