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Theorem elimdhyp 4005
Description: Version of elimhyp 4000 where the hypothesis is deduced from the final antecedent. See ghomgrplem 29029 for an example of its use. (Contributed by Paul Chapman, 25-Mar-2008.)
Hypotheses
Ref Expression
elimdhyp.1
elimdhyp.2
elimdhyp.3
elimdhyp.4
Assertion
Ref Expression
elimdhyp

Proof of Theorem elimdhyp
StepHypRef Expression
1 elimdhyp.1 . . 3
2 iftrue 3947 . . . . 5
32eqcomd 2465 . . . 4
4 elimdhyp.2 . . . 4
53, 4syl 16 . . 3
61, 5mpbid 210 . 2
7 elimdhyp.4 . . 3
8 iffalse 3950 . . . . 5
98eqcomd 2465 . . . 4
10 elimdhyp.3 . . . 4
119, 10syl 16 . . 3
127, 11mpbii 211 . 2
136, 12pm2.61i 164 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  =wceq 1395  ifcif 3941
This theorem is referenced by:  divalg  14061  ghomgrplem  29029
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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