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Theorem a12studyALT 29755
 Description: Alternate proof of a12study 29754, also without using ax12o 1887. (Contributed by NM, 17-Jan-2008.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
a12study.1
a12study.2
Assertion
Ref Expression
a12studyALT

Proof of Theorem a12studyALT
StepHypRef Expression
1 hbn1 1716 . . . . 5
2 hbn1 1716 . . . . 5
31, 2hban 1748 . . . 4
4 a12study.1 . . . . . 6
54con3d 125 . . . . 5
6 exnal 1564 . . . . . 6
7 hba1 1731 . . . . . . 7
8 annim 414 . . . . . . . 8
9 ax11o 1947 . . . . . . . . . 10
10 a12study.2 . . . . . . . . . . 11
1110a5i 1770 . . . . . . . . . 10
129, 11syl8 65 . . . . . . . . 9
1312imp3a 420 . . . . . . . 8
148, 13syl5bir 209 . . . . . . 7
151, 7, 14exlimdh 1816 . . . . . 6
166, 15syl5bir 209 . . . . 5
175, 16sylan9r 639 . . . 4
183, 17hbnd 1836 . . 3
19 notnot 282 . . 3
2019albii 1556 . . 3
2118, 19, 203imtr4g 261 . 2
2221ex 423 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 358  wal 1530  wex 1531 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-nf 1535
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