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Theorem pm14.123b 31280
 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 31270 . . . 4
21adantr 465 . . 3
3 nfa1 1881 . . . . 5
4 nfa2 1937 . . . . . 6
5 simpr 461 . . . . . . 7
6 2sp 1850 . . . . . . . 8
76ancrd 554 . . . . . . 7
85, 7impbid2 204 . . . . . 6
94, 8exbid 1870 . . . . 5
103, 9exbid 1870 . . . 4
1110adantl 466 . . 3
122, 11bitr3d 255 . 2
1312pm5.32da 641 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369  wal 1379   wceq 1381  wex 1597   wcel 1802  wsbc 3311 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1603  ax-4 1616  ax-5 1689  ax-6 1732  ax-7 1774  ax-10 1821  ax-11 1826  ax-12 1838  ax-13 1983  ax-ext 2419 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1384  df-ex 1598  df-nf 1602  df-sb 1725  df-clab 2427  df-cleq 2433  df-clel 2436  df-nfc 2591  df-v 3095  df-sbc 3312 This theorem is referenced by:  pm14.123c  31281
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