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Theorem pm14.122b 31492
 Description: Theorem *14.122 in [WhiteheadRussell] p. 185. (Contributed by Andrew Salmon, 9-Jun-2011.)
Assertion
Ref Expression
pm14.122b
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem pm14.122b
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eqeq2 2472 . . . . . 6
21imbi2d 316 . . . . 5
32albidv 1714 . . . 4
4 dfsbcq 3329 . . . . 5
54bibi1d 319 . . . 4
63, 5imbi12d 320 . . 3
7 sbc5 3352 . . . 4
8 nfa1 1898 . . . . 5
9 simpr 461 . . . . . 6
10 ancr 549 . . . . . . 7
1110sps 1866 . . . . . 6
129, 11impbid2 204 . . . . 5
138, 12exbid 1887 . . . 4
147, 13syl5bb 257 . . 3
156, 14vtoclg 3167 . 2
1615pm5.32d 639 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369  wal 1393   wceq 1395  wex 1613   wcel 1819  wsbc 3327 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-12 1855  ax-13 2000  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111  df-sbc 3328 This theorem is referenced by:  pm14.122c  31493
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