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Theorem 3eltr4i 2116
Description: Substitution of equal classes into membership relation. (Contributed by Mario Carneiro, 6-Jan-2017.)
Hypotheses
Ref Expression
3eltr4.1 A B
3eltr4.2 𝐶 = A
3eltr4.3 𝐷 = B
Assertion
Ref Expression
3eltr4i 𝐶 𝐷

Proof of Theorem 3eltr4i
StepHypRef Expression
1 3eltr4.2 . 2 𝐶 = A
2 3eltr4.1 . . 3 A B
3 3eltr4.3 . . 3 𝐷 = B
42, 3eleqtrri 2110 . 2 A 𝐷
51, 4eqeltri 2107 1 𝐶 𝐷
Colors of variables: wff set class
Syntax hints:   = wceq 1242   wcel 1390
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-cleq 2030  df-clel 2033
This theorem is referenced by:  1nq  6350  0r  6658  1sr  6659  m1r  6660
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