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Theorem elimdhyp 4009
 Description: Version of elimhyp 4004 where the hypothesis is deduced from the final antecedent. See ghomgrplem 28854 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 3951 . . . . 5
32eqcomd 2475 . . . 4
4 elimdhyp.2 . . . 4
53, 4syl 16 . . 3
61, 5mpbid 210 . 2
7 elimdhyp.4 . . 3
8 iffalse 3954 . . . . 5
98eqcomd 2475 . . . 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 1379  cif 3945 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-if 3946 This theorem is referenced by:  divalg  13937  ghomgrplem  28854
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