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Theorem dedth4h 3928
 Description: Weak deduction theorem eliminating four hypotheses. See comments in dedth2h 3926. (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 3926 . . 3
92, 4, 8dedth2h 3926 . 2
109imp 429 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   wceq 1370  cif 3875 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1709  ax-7 1729  ax-10 1776  ax-11 1781  ax-12 1793  ax-13 1944  ax-ext 2429 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1702  df-clab 2436  df-cleq 2442  df-clel 2445  df-if 3876 This theorem is referenced by:  dedth4v  3931  fprg  5976  omopth  7183  nn0opth2  12137  ax5seglem8  23303  hvsubsub4  24583  norm3lemt  24675  eigorth  25363
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