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Theorem pm14.122b 27591
 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 2444 . . . . . 6
21imbi2d 308 . . . . 5
32albidv 1635 . . . 4
4 dfsbcq 3155 . . . . 5
54bibi1d 311 . . . 4
63, 5imbi12d 312 . . 3
7 sbc5 3177 . . . 4
8 nfa1 1806 . . . . 5
9 simpr 448 . . . . . 6
10 ancr 533 . . . . . . 7
1110sps 1770 . . . . . 6
129, 11impbid2 196 . . . . 5
138, 12exbid 1789 . . . 4
147, 13syl5bb 249 . . 3
156, 14vtoclg 3003 . 2
1615pm5.32d 621 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549  wex 1550   wceq 1652   wcel 1725  wsbc 3153 This theorem is referenced by:  pm14.122c  27592 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-sbc 3154
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