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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
StepHypRef Expression
1 3eltr4.2 . 2
2 3eltr4.1 . . 3
3 3eltr4.3 . . 3
42, 3eleqtrri 2544 . 2
51, 4eqeltri 2541 1
 Colors of variables: wff setvar class 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
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