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Theorem dvelimf-o 2264
 Description: Proof of dvelimh 2075 that uses ax-10o 2223 but not ax-11o 2225, ax-10 2224, or ax-11 1764. Version of dvelimh 2075 using ax-10o 2223 instead of ax10o 2042. (Contributed by NM, 12-Nov-2002.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
dvelimf-o.1
dvelimf-o.2
dvelimf-o.3
Assertion
Ref Expression
dvelimf-o

Proof of Theorem dvelimf-o
StepHypRef Expression
1 hba1-o 2233 . . . . 5
2 ax-10o 2223 . . . . . 6
32aecoms-o 2236 . . . . 5
41, 3syl5 31 . . . 4
54a1d 24 . . 3
6 hbnae-o 2263 . . . . . 6
7 hbnae-o 2263 . . . . . 6
86, 7hban 1853 . . . . 5
9 hbnae-o 2263 . . . . . . 7
10 hbnae-o 2263 . . . . . . 7
119, 10hban 1853 . . . . . 6
12 ax-12o 2226 . . . . . . 7
1312imp 420 . . . . . 6
14 dvelimf-o.1 . . . . . . 7
1514a1i 11 . . . . . 6
1611, 13, 15hbimd 1837 . . . . 5
178, 16hbald 1758 . . . 4
1817ex 425 . . 3
195, 18pm2.61i 159 . 2
20 dvelimf-o.2 . . 3
21 dvelimf-o.3 . . 3
2220, 21equsalh 2005 . 2
2322albii 1576 . 2
2419, 22, 233imtr3g 262 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178   wa 360  wal 1550 This theorem is referenced by:  dveeq2-o  2268  dveeq1-o  2271  ax11el  2278 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 1628  ax-9 1669  ax-8 1690  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-4 2219  ax-5o 2220  ax-6o 2221  ax-10o 2223  ax-12o 2226 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-nf 1555
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