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Theorem pm14.123b 26793
 Description: Theorem *14.123 in [WhiteheadRussell] p. 185. (Contributed by Andrew Salmon, 9-Jun-2011.)
Assertion
Ref Expression
pm14.123b
Distinct variable groups:   ,,   ,,
Allowed substitution hints:   (,)   (,)   (,)

Proof of Theorem pm14.123b
StepHypRef Expression
1 2sbc5g 26783 . . . 4
3 nfa1 1719 . . . . 5
4 nfa2 1744 . . . . . 6
5 simpr 449 . . . . . . 7
6 ax-4 1692 . . . . . . . . 9
76a4s 1700 . . . . . . . 8
87ancrd 539 . . . . . . 7
95, 8impbid2 197 . . . . . 6
104, 9exbid 1714 . . . . 5
113, 10exbid 1714 . . . 4
132, 12bitr3d 248 . 2
1413pm5.32da 625 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178   wa 360  wal 1532  wex 1537   wceq 1619   wcel 1621  wsbc 2921 This theorem is referenced by:  pm14.123c  26794 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-v 2729  df-sbc 2922
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