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Theorem syl6eleqr 2444
 Description: A membership and equality inference. (Contributed by NM, 24-Apr-2005.)
Hypotheses
Ref Expression
syl6eleqr.1 (φA B)
syl6eleqr.2 C = B
Assertion
Ref Expression
syl6eleqr (φA C)

Proof of Theorem syl6eleqr
StepHypRef Expression
1 syl6eleqr.1 . 2 (φA B)
2 syl6eleqr.2 . . 3 C = B
32eqcomi 2357 . 2 B = C
41, 3syl6eleq 2443 1 (φA 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:  reiotacl2  4363  nnadjoinpw  4521  sfinltfin  4535  vinf  4555  nulnnn  4556  ecopqsi  5981  ncidg  6122
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