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Theorem dedth4h 3996
 Description: Weak deduction theorem eliminating four hypotheses. See comments in dedth2h 3994. (Contributed by NM, 16-May-1999.)
Hypotheses
Ref Expression
dedth4h.1
dedth4h.2
dedth4h.3
dedth4h.4
dedth4h.5
Assertion
Ref Expression
dedth4h

Proof of Theorem dedth4h
StepHypRef Expression
1 dedth4h.1 . . . 4
21imbi2d 316 . . 3
3 dedth4h.2 . . . 4
43imbi2d 316 . . 3
5 dedth4h.3 . . . 4
6 dedth4h.4 . . . 4
7 dedth4h.5 . . . 4
85, 6, 7dedth2h 3994 . . 3
92, 4, 8dedth2h 3994 . 2
109imp 429 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  ifcif 3941 This theorem is referenced by:  dedth4v  3999  fprg  6080  omopth  7326  nn0opth2  12352  ax5seglem8  24239  hvsubsub4  25977  norm3lemt  26069  eigorth  26757 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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