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Theorem syl6eqelr 2126
Description: A membership and equality inference. (Contributed by NM, 4-Jan-2006.)
Hypotheses
Ref Expression
syl6eqelr.1 (φB = A)
syl6eqelr.2 B 𝐶
Assertion
Ref Expression
syl6eqelr (φA 𝐶)

Proof of Theorem syl6eqelr
StepHypRef Expression
1 syl6eqelr.1 . . 3 (φB = A)
21eqcomd 2042 . 2 (φA = B)
3 syl6eqelr.2 . 2 B 𝐶
42, 3syl6eqel 2125 1 (φA 𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1242   wcel 1390
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-cleq 2030  df-clel 2033
This theorem is referenced by:  eusvnfb  4152  releldm2  5753  bren  6164  brdomg  6165  ioof  8610
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