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Theorem 3eltr3i 2431
Description: Substitution of equal classes into membership relation. (Contributed by Mario Carneiro, 6-Jan-2017.)
Hypotheses
Ref Expression
3eltr3.1 A B
3eltr3.2 A = C
3eltr3.3 B = D
Assertion
Ref Expression
3eltr3i C D

Proof of Theorem 3eltr3i
StepHypRef Expression
1 3eltr3.2 . 2 A = C
2 3eltr3.1 . . 3 A B
3 3eltr3.3 . . 3 B = D
42, 3eleqtri 2425 . 2 A D
51, 4eqeltrri 2424 1 C D
Colors of variables: wff setvar class
Syntax hints:   = wceq 1642   wcel 1710
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-cleq 2346  df-clel 2349
This theorem is referenced by: (None)
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