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Theorem dral1 2067
 Description: Formula-building lemma for use with the Distinctor Reduction Theorem. Part of Theorem 9.4 of [Megill] p. 448 (p. 16 of preprint). (Contributed by NM, 24-Nov-1994.) Remove dependency on ax-11 1842. (Revised by Wolf Lammen, 6-Sep-2018.)
Hypothesis
Ref Expression
dral1.1
Assertion
Ref Expression
dral1

Proof of Theorem dral1
StepHypRef Expression
1 nfa1 1897 . . 3
2 dral1.1 . . 3
31, 2albid 1885 . 2
4 axc11 2054 . . 3
5 axc112 1937 . . 3
64, 5impbid 191 . 2
73, 6bitrd 253 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  A.wal 1393 This theorem is referenced by:  drex1  2069  drnf1  2071  axc16gALT  2106  sb9  2169  ralcom2  3022  axpownd  8999  wl-dral1d  29984  wl-ax11-lem5  30029  wl-ax11-lem8  30032  wl-ax11-lem9  30033 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854  ax-13 1999 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617
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