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Theorem releqi 4451
 Description: Equality inference for the relation predicate. (Contributed by NM, 8-Dec-2006.)
Hypothesis
Ref Expression
releqi.1 𝐴 = 𝐵
Assertion
Ref Expression
releqi (Rel 𝐴 ↔ Rel 𝐵)

Proof of Theorem releqi
StepHypRef Expression
1 releqi.1 . 2 𝐴 = 𝐵
2 releq 4450 . 2 (𝐴 = 𝐵 → (Rel 𝐴 ↔ Rel 𝐵))
31, 2ax-mp 7 1 (Rel 𝐴 ↔ Rel 𝐵)
 Colors of variables: wff set class Syntax hints:   ↔ wb 102   = wceq 1259  Rel wrel 4378 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-in 2952  df-ss 2959  df-rel 4380 This theorem is referenced by:  reliun  4486  reluni  4488  relint  4489  reldmmpt2  5640  tfrlem6  5963
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