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Theorem pm13.192 27520
 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 190 . . . . . . 7
21alimi 1568 . . . . . 6
3 nfv 1629 . . . . . . 7
4 eqeq1 2436 . . . . . . 7
53, 4equsal 1999 . . . . . 6
62, 5sylib 189 . . . . 5
7 eqeq2 2439 . . . . . . 7
87eqcoms 2433 . . . . . 6
98alrimiv 1641 . . . . 5
106, 9impbii 181 . . . 4
1110anbi1i 677 . . 3
1211exbii 1592 . 2
13 sbc5 3172 . 2
1412, 13bitr4i 244 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549  wex 1550   wceq 1652  wsbc 3148 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 2411 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 2417  df-cleq 2423  df-clel 2426  df-nfc 2555  df-v 2945  df-sbc 3149
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