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Theorem eqeltrrd 2428
 Description: Deduction that substitutes equal classes into membership. (Contributed by NM, 14-Dec-2004.)
Hypotheses
Ref Expression
eqeltrrd.1 (φA = B)
eqeltrrd.2 (φA C)
Assertion
Ref Expression
eqeltrrd (φB C)

Proof of Theorem eqeltrrd
StepHypRef Expression
1 eqeltrrd.1 . . 3 (φA = B)
21eqcomd 2358 . 2 (φB = A)
3 eqeltrrd.2 . 2 (φA C)
42, 3eqeltrd 2427 1 (φB C)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642   ∈ wcel 1710 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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:  3eltr3d  2433  nnsucelr  4428  sfinltfin  4535  vfin1cltv  4547  vfinspsslem1  4550  phi11lem1  4595  xpexr2  5110  ffvresb  5431  ncdisjun  6136  eqtc  6161
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