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Theorem 3eltr3g 2561
 Description: Substitution of equal classes into membership relation. (Contributed by Mario Carneiro, 6-Jan-2017.) (Proof shortened by Wolf Lammen, 23-Nov-2019.)
Hypotheses
Ref Expression
3eltr3g.1
3eltr3g.2
3eltr3g.3
Assertion
Ref Expression
3eltr3g

Proof of Theorem 3eltr3g
StepHypRef Expression
1 3eltr3g.2 . . 3
2 3eltr3g.1 . . 3
31, 2syl5eqelr 2550 . 2
4 3eltr3g.3 . 2
53, 4syl6eleq 2555 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  =wceq 1395  e.wcel 1818 This theorem is referenced by:  rankelpr  8312  isf34lem7  8780  rmulccn  27910  xrge0mulc1cn  27923  esumpfinvallem  28080  fourierdlem62  31951 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-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-cleq 2449  df-clel 2452
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