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Theorem proplem2 13904
 Description: Lemma for mndpropd 14711. (Contributed by Mario Carneiro, 6-Dec-2014.)
Assertion
Ref Expression
proplem2
Distinct variable groups:   ,,   ,,   ,,   ,,   ,   ,,
Allowed substitution hint:   ()

Proof of Theorem proplem2
StepHypRef Expression
1 oveq1 6080 . . 3
21eleq1d 2501 . 2
3 oveq2 6081 . . 3
43eleq1d 2501 . 2
52, 4rspc2va 3051 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652   wcel 1725  wral 2697  (class class class)co 6073 This theorem is referenced by:  mndpropd  14711  issubmnd  14714  submcl  14743  issubg2  14949  gass  15068  lmodprop2d  15996  lsspropd  16083  off2  24044  ofcf  24476 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 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 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-iota 5410  df-fv 5454  df-ov 6076
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