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Theorem elimdelov 5927
 Description: Eliminate a hypothesis which is a predicate expressing membership in the result of an operator (deduction version). See ghomgrplem 23996 for an example of its use. (Contributed by Paul Chapman, 25-Mar-2008.)
Hypotheses
Ref Expression
elimdelov.1
elimdelov.2
Assertion
Ref Expression
elimdelov

Proof of Theorem elimdelov
StepHypRef Expression
1 iftrue 3571 . . . 4
2 elimdelov.1 . . . 4
31, 2eqeltrd 2357 . . 3
4 iftrue 3571 . . . 4
5 iftrue 3571 . . . 4
64, 5oveq12d 5876 . . 3
73, 6eleqtrrd 2360 . 2
8 iffalse 3572 . . . 4
9 elimdelov.2 . . . 4
108, 9syl6eqel 2371 . . 3
11 iffalse 3572 . . . 4
12 iffalse 3572 . . . 4
1311, 12oveq12d 5876 . . 3
1410, 13eleqtrrd 2360 . 2
157, 14pm2.61i 156 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wcel 1684  cif 3565  (class class class)co 5858 This theorem is referenced by:  ghomgrplem  23996 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-iota 5219  df-fv 5263  df-ov 5861
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