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Theorem 3eltr3g 2518
 Description: Substitution of equal classes into membership relation. (Contributed by Mario Carneiro, 6-Jan-2017.)
Hypotheses
Ref Expression
3eltr3g.1
3eltr3g.2
3eltr3g.3
Assertion
Ref Expression
3eltr3g

Proof of Theorem 3eltr3g
StepHypRef Expression
1 3eltr3g.1 . 2
2 3eltr3g.2 . . 3
3 3eltr3g.3 . . 3
42, 3eleq12i 2501 . 2
51, 4sylib 189 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725 This theorem is referenced by:  rankelpr  7799  isf34lem7  8259  rmulccn  24314  xrge0mulc1cn  24327  esumpfinvallem  24464 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-11 1761  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-cleq 2429  df-clel 2432
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