Theorem 3eltr4i 2714

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

Hypotheses

Ref	Expression
3eltr4.1	|- A e. B
3eltr4.2	|- C = A
3eltr4.3	|- D = B

Assertion

Ref	Expression
3eltr4i	|- C e. D

Proof of Theorem 3eltr4i

Step	Hyp	Ref	Expression
1		3eltr4.2	. 2 |- C = A
2		3eltr4.1	. . 3 |- A e. B
3		3eltr4.3	. . 3 |- D = B
4	2, 3	eleqtrri 2700	. 2 |- A e. D
5	1, 4	eqeltri 2697	1 |- C e. D

Syntax hints:   = wceq 1483   e. wcel 1990

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-cleq 2615  df-clel 2618

This theorem is referenced by:  oancom  8548  0r  9901  1sr  9902  m1r  9903  recvs  22946  qcvs  22947  wlk2v2elem1  27015  konigsbergiedgw  27108  konigsbergiedgwOLD  27109  lmxrge0  29998  brsigarn  30247  sinccvglem  31566  bj-minftyccb  33112  fouriersw  40448