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Theorem keephyp 4006
 Description: Transform a hypothesis that we want to keep (but contains the same class variable used in the eliminated hypothesis) for use with the weak deduction theorem. (Contributed by NM, 15-May-1999.)
Hypotheses
Ref Expression
keephyp.1
keephyp.2
keephyp.3
keephyp.4
Assertion
Ref Expression
keephyp

Proof of Theorem keephyp
StepHypRef Expression
1 keephyp.3 . 2
2 keephyp.4 . 2
3 keephyp.1 . . 3
4 keephyp.2 . . 3
53, 4ifboth 3977 . 2
61, 2, 5mp2an 672 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  ifcif 3941 This theorem is referenced by:  keepel  4009  boxcutc  7532  fin23lem13  8733  abvtrivd  17489  znf1o  18590  zntoslem  18595  dscmet  21093  sqff1o  23456  lgsne0  23608  dchrisum0flblem1  23693  dchrisum0flblem2  23694 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-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-if 3942
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