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Theorem eleqtrrd 2430
 Description: Deduction that substitutes equal classes into membership. (Contributed by NM, 14-Dec-2004.)
Hypotheses
Ref Expression
eleqtrrd.1 (φA B)
eleqtrrd.2 (φC = B)
Assertion
Ref Expression
eleqtrrd (φA C)

Proof of Theorem eleqtrrd
StepHypRef Expression
1 eleqtrrd.1 . 2 (φA B)
2 eleqtrrd.2 . . 3 (φC = B)
32eqcomd 2358 . 2 (φB = C)
41, 3eleqtrd 2429 1 (φA C)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = 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:  3eltr4d  2434  tfin11  4493  tfinnn  4534  fvopab4t  5385  elimdelov  5573  enadjlem1  6059  enprmaplem3  6078  pw1eltc  6162  spacid  6285  spaccl  6286  frecsuc  6322
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