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Theorem elimdelov 6378
Description: Eliminate a hypothesis which is a predicate expressing membership in the result of an operator (deduction version). See ghomgrplem 29029 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 elimdelov.1 . . 3
2 iftrue 3947 . . 3
3 iftrue 3947 . . . 4
4 iftrue 3947 . . . 4
53, 4oveq12d 6314 . . 3
61, 2, 53eltr4d 2560 . 2
7 iffalse 3950 . . . 4
8 elimdelov.2 . . . 4
97, 8syl6eqel 2553 . . 3
10 iffalse 3950 . . . 4
11 iffalse 3950 . . . 4
1210, 11oveq12d 6314 . . 3
139, 12eleqtrrd 2548 . 2
146, 13pm2.61i 164 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  e.wcel 1818  ifcif 3941  (class class class)co 6296
This theorem is referenced by:  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-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-iota 5556  df-fv 5601  df-ov 6299
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