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Theorem caovdilem 6274
 Description: Lemma used by 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
Assertion
Ref Expression
caovdilem
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,   ,,,

Proof of Theorem caovdilem
StepHypRef Expression
1 ovex 6098 . . 3
2 ovex 6098 . . 3
3 caovdl.5 . . 3
4 caovdir.com . . 3
5 caovdir.distr . . 3
61, 2, 3, 4, 5caovdir 6273 . 2
7 caovdir.1 . . . 4
8 caovdir.3 . . . 4
9 caovdl.ass . . . 4
107, 8, 3, 9caovass 6239 . . 3
11 caovdir.2 . . . 4
12 caovdl.4 . . . 4
1311, 12, 3, 9caovass 6239 . . 3
1410, 13oveq12i 6085 . 2
156, 14eqtri 2455 1
 Colors of variables: wff set class Syntax hints:   wceq 1652   wcel 1725  cvv 2948  (class class class)co 6073 This theorem is referenced by:  caovlem2  6275  axmulass  9024 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-nul 4330 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-iota 5410  df-fv 5454  df-ov 6076
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