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Theorem releqd 4424
 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 4422 . 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 98   = wceq 1243  Rel wrel 4350 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 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-in 2924  df-ss 2931  df-rel 4352 This theorem is referenced by:  dftpos3  5877  tposfo2  5882  tposf12  5884
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