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Theorem 3eltr4i 2701
 Description: Substitution of equal classes into membership relation. (Contributed by Mario Carneiro, 6-Jan-2017.)
Hypotheses
Ref Expression
3eltr4.1 𝐴𝐵
3eltr4.2 𝐶 = 𝐴
3eltr4.3 𝐷 = 𝐵
Assertion
Ref Expression
3eltr4i 𝐶𝐷

Proof of Theorem 3eltr4i
StepHypRef Expression
1 3eltr4.2 . 2 𝐶 = 𝐴
2 3eltr4.1 . . 3 𝐴𝐵
3 3eltr4.3 . . 3 𝐷 = 𝐵
42, 3eleqtrri 2687 . 2 𝐴𝐷
51, 4eqeltri 2684 1 𝐶𝐷
 Colors of variables: wff setvar class Syntax hints:   = wceq 1475   ∈ wcel 1977 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696  df-cleq 2603  df-clel 2606 This theorem is referenced by:  oancom  8431  0r  9780  1sr  9781  m1r  9782  recvs  22754  qcvs  22755  lmxrge0  29326  brsigarn  29574  sinccvglem  30820  bj-minftyccb  32289  fouriersw  39124  1wlk2v2elem1  41322  konigsbergiedgw  41416  konigsbergiedgwOLD  41417
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