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Theorem resoprab2 6160
 Description: Restriction of an operator abstraction. (Contributed by Jeff Madsen, 2-Sep-2009.)
Assertion
Ref Expression
resoprab2
Distinct variable groups:   ,,,   ,,,   ,,,   ,,,
Allowed substitution hints:   (,,)

Proof of Theorem resoprab2
StepHypRef Expression
1 resoprab 6159 . 2
2 anass 631 . . . 4
3 an4 798 . . . . . 6
4 ssel 3335 . . . . . . . . 9
54pm4.71d 616 . . . . . . . 8
65bicomd 193 . . . . . . 7
7 ssel 3335 . . . . . . . . 9
87pm4.71d 616 . . . . . . . 8
98bicomd 193 . . . . . . 7
106, 9bi2anan9 844 . . . . . 6
113, 10syl5bb 249 . . . . 5
1211anbi1d 686 . . . 4
132, 12syl5bbr 251 . . 3
1413oprabbidv 6121 . 2
151, 14syl5eq 2480 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652   wcel 1725   wss 3313   cxp 4869   cres 4873  coprab 6075 This theorem is referenced by:  resmpt2  6161 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4323  ax-nul 4331  ax-pr 4396 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2703  df-rex 2704  df-rab 2707  df-v 2951  df-dif 3316  df-un 3318  df-in 3320  df-ss 3327  df-nul 3622  df-if 3733  df-sn 3813  df-pr 3814  df-op 3816  df-opab 4260  df-xp 4877  df-rel 4878  df-res 4883  df-oprab 6078
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