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Theorem caovlem2 6285
 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 6108 . . 3
2 ovex 6108 . . 3
3 ovex 6108 . . 3
4 caovdl2.com . . 3
5 caovdl2.ass . . 3
6 ovex 6108 . . 3
71, 2, 3, 4, 5, 6caov42 6282 . 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 6284 . . 3
17 caovdl2.6 . . . 4
188, 9, 13, 11, 12, 10, 17, 15caovdilem 6284 . . 3
1916, 18oveq12i 6095 . 2
20 ovex 6108 . . . 4
21 ovex 6108 . . . 4
228, 20, 21, 12caovdi 6268 . . 3
23 ovex 6108 . . . 4
24 ovex 6108 . . . 4
259, 23, 24, 12caovdi 6268 . . 3
2622, 25oveq12i 6095 . 2
277, 19, 263eqtr4i 2468 1
 Colors of variables: wff set class Syntax hints:   wceq 1653   wcel 1726  cvv 2958  (class class class)co 6083 This theorem is referenced by:  mulasssr  8967 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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  ax-nul 4340 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-eu 2287  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-sbc 3164  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 4215  df-iota 5420  df-fv 5464  df-ov 6086
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