Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  caovdi Unicode version

Theorem caovdi 5680
 Description: Convert an operation distributive law to class notation. (Contributed by NM, 25-Aug-1995.) (Revised by Mario Carneiro, 28-Jun-2013.)
Hypotheses
Ref Expression
caovdi.1
caovdi.2
caovdi.3
caovdi.4
Assertion
Ref Expression
caovdi
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caovdi
StepHypRef Expression
1 caovdi.1 . 2
2 caovdi.2 . 2
3 caovdi.3 . 2
4 tru 1247 . . 3
5 caovdi.4 . . . . 5
65a1i 9 . . . 4
76caovdig 5675 . . 3
84, 7mpan 400 . 2
91, 2, 3, 8mp3an 1232 1
 Colors of variables: wff set class Syntax hints:   wa 97   w3a 885   wceq 1243   wtru 1244   wcel 1393  cvv 2557  (class class class)co 5512 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382  df-op 3384  df-uni 3581  df-br 3765  df-iota 4867  df-fv 4910  df-ov 5515 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator