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Theorem dvelimf-o 2180
 Description: Proof of dvelimh 1964 that uses ax-10o 2139 but not ax-11o 2141, ax-10 2140, or ax-11 1746. Version of dvelimh 1964 using ax-10o 2139 instead of ax10o 1952. (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 2149 . . . . 5
2 ax-10o 2139 . . . . . 6
32aecoms-o 2152 . . . . 5
41, 3syl5 28 . . . 4
54a1d 22 . . 3
6 hbnae-o 2179 . . . . . 6
7 hbnae-o 2179 . . . . . 6
86, 7hban 1828 . . . . 5
9 hbnae-o 2179 . . . . . . 7
10 hbnae-o 2179 . . . . . . 7
119, 10hban 1828 . . . . . 6
12 ax-12o 2142 . . . . . . 7
1312imp 418 . . . . . 6
14 dvelimf-o.1 . . . . . . 7
1514a1i 10 . . . . . 6
1611, 13, 15hbimd 1815 . . . . 5
178, 16hbald 1740 . . . 4
1817ex 423 . . 3
195, 18pm2.61i 156 . 2
20 dvelimf-o.2 . . 3
21 dvelimf-o.3 . . 3
2220, 21equsalh 1961 . 2
2322albii 1566 . 2
2419, 22, 233imtr3g 260 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 176   wa 358  wal 1540 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-4 2135  ax-5o 2136  ax-6o 2137  ax-10o 2139  ax-12o 2142 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545 This theorem is referenced by:  dveeq2-o  2184  dveeq1-o  2187  ax11el  2194
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