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Theorem dedth4h 3784
 Description: Weak deduction theorem eliminating four hypotheses. See comments in dedth2h 3782. (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 309 . . 3
3 dedth4h.2 . . . 4
43imbi2d 309 . . 3
5 dedth4h.3 . . . 4
6 dedth4h.4 . . . 4
7 dedth4h.5 . . . 4
85, 6, 7dedth2h 3782 . . 3
92, 4, 8dedth2h 3782 . 2
109imp 420 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   wceq 1653  cif 3740 This theorem is referenced by:  dedth4v  3787  fprg  5916  omopth  6902  nn0opth2  11566  hvsubsub4  22563  norm3lemt  22655  eigorth  23342  ax5seglem8  25876 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-if 3741
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