Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  caovlem2 Unicode version

Theorem caovlem2 6511
 Description: Lemma used in real number construction. (Contributed by NM, 26-Aug-1995.)
Hypotheses
Ref Expression
caovdir.1
caovdir.2
caovdir.3
caovdir.com
caovdir.distr
caovdl.4
caovdl.5
caovdl.ass
caovdl2.6
caovdl2.com
caovdl2.ass
Assertion
Ref Expression
caovlem2
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caovlem2
StepHypRef Expression
1 ovex 6324 . . 3
2 ovex 6324 . . 3
3 ovex 6324 . . 3
4 caovdl2.com . . 3
5 caovdl2.ass . . 3
6 ovex 6324 . . 3
71, 2, 3, 4, 5, 6caov42 6508 . 2
8 caovdir.1 . . . 4
9 caovdir.2 . . . 4
10 caovdir.3 . . . 4
11 caovdir.com . . . 4
12 caovdir.distr . . . 4
13 caovdl.4 . . . 4
14 caovdl.5 . . . 4
15 caovdl.ass . . . 4
168, 9, 10, 11, 12, 13, 14, 15caovdilem 6510 . . 3
17 caovdl2.6 . . . 4
188, 9, 13, 11, 12, 10, 17, 15caovdilem 6510 . . 3
1916, 18oveq12i 6308 . 2
20 ovex 6324 . . . 4
21 ovex 6324 . . . 4
228, 20, 21, 12caovdi 6494 . . 3
23 ovex 6324 . . . 4
24 ovex 6324 . . . 4
259, 23, 24, 12caovdi 6494 . . 3
2622, 25oveq12i 6308 . 2
277, 19, 263eqtr4i 2496 1
 Colors of variables: wff setvar class Syntax hints:  =wceq 1395  e.wcel 1818   cvv 3109  (class class class)co 6296 This theorem is referenced by:  mulasssr  9488 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  ax-nul 4581 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-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-iota 5556  df-fv 5601  df-ov 6299
 Copyright terms: Public domain W3C validator