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Theorem 3eltr4i 2711
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 2697 . 2 𝐴𝐷
51, 4eqeltri 2694 1 𝐶𝐷
Colors of variables: wff setvar class
Syntax hints:   = wceq 1480  wcel 1987
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1702  df-cleq 2614  df-clel 2617
This theorem is referenced by:  oancom  8492  0r  9845  1sr  9846  m1r  9847  recvs  22854  qcvs  22855  wlk2v2elem1  26881  konigsbergiedgw  26974  konigsbergiedgwOLD  26975  lmxrge0  29780  brsigarn  30028  sinccvglem  31274  bj-minftyccb  32745  fouriersw  39755
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