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Theorem releqd 4631
 Description: Equality deduction for the relation predicate. (Contributed by NM, 8-Mar-2014.)
Hypothesis
Ref Expression
releqd.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
releqd (𝜑 → (Rel 𝐴 ↔ Rel 𝐵))

Proof of Theorem releqd
StepHypRef Expression
1 releqd.1 . 2 (𝜑𝐴 = 𝐵)
2 releq 4629 . 2 (𝐴 = 𝐵 → (Rel 𝐴 ↔ Rel 𝐵))
31, 2syl 14 1 (𝜑 → (Rel 𝐴 ↔ Rel 𝐵))
 Colors of variables: wff set class Syntax hints:   → wi 4   ↔ wb 104   = wceq 1332  Rel wrel 4552 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-11 1485  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-in 3082  df-ss 3089  df-rel 4554 This theorem is referenced by:  dftpos3  6167  tposfo2  6172  tposf12  6174  lmreltop  12402  cnprcl2k  12415
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