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Theorem releqd 4452
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 4450 . 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 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:  dftpos3  5908  tposfo2  5913  tposf12  5915
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