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Theorem pm13.192 26777
 Description: Theorem *13.192 in [WhiteheadRussell] p. 179. (Contributed by Andrew Salmon, 3-Jun-2011.) (Revised by NM, 4-Jan-2017.)
Assertion
Ref Expression
pm13.192
Distinct variable group:   ,,
Allowed substitution hints:   (,)

Proof of Theorem pm13.192
StepHypRef Expression
1 bi2 191 . . . . . . 7
21alimi 1546 . . . . . 6
3 nfv 1629 . . . . . . 7
4 eqeq1 2259 . . . . . . 7
53, 4equsal 1850 . . . . . 6
62, 5sylib 190 . . . . 5
7 eqeq2 2262 . . . . . . 7
87eqcoms 2256 . . . . . 6
98alrimiv 2012 . . . . 5
106, 9impbii 182 . . . 4
1110anbi1i 679 . . 3
1211exbii 1580 . 2
13 sbc5 2945 . 2
1412, 13bitr4i 245 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178   wa 360  wal 1532  wex 1537   wceq 1619  wsbc 2921 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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