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

Step	Hyp	Ref	Expression
1		3eltr3g.2	. . 3
2		3eltr3g.1	. . 3
3	1, 2	syl5eqelr 2550	. 2
4		3eltr3g.3	. 2
5	3, 4	syl6eleq 2555	1

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