Theorem 3eltr4i 2558

Description: Substitution of equal classes into membership relation. (Contributed by Mario Carneiro, 6-Jan-2017.)

Hypotheses

Ref	Expression
3eltr4.1
3eltr4.2
3eltr4.3

Assertion

Ref	Expression
3eltr4i

Proof of Theorem 3eltr4i

Step	Hyp	Ref	Expression
1		3eltr4.2	. 2
2		3eltr4.1	. . 3
3		3eltr4.3	. . 3
4	2, 3	eleqtrri 2544	. 2
5	1, 4	eqeltri 2541	1

Syntax hints:  =wceq 1395  e.wcel 1818

This theorem is referenced by:  oancom  8089  0r  9478  1sr  9479  m1r  9480  lmxrge0  27934  brsigarn  28155  sinccvglem  29038  fouriersw  32014  bj-minftyccb  34628

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