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Theorem sbceq1d 2848
 Description: Equality theorem for class substitution. (Contributed by Mario Carneiro, 9-Feb-2017.) (Revised by NM, 30-Jun-2018.)
Hypothesis
Ref Expression
sbceq1d.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
sbceq1d (𝜑 → ([𝐴 / 𝑥]𝜓[𝐵 / 𝑥]𝜓))

Proof of Theorem sbceq1d
StepHypRef Expression
1 sbceq1d.1 . 2 (𝜑𝐴 = 𝐵)
2 dfsbcq 2845 . 2 (𝐴 = 𝐵 → ([𝐴 / 𝑥]𝜓[𝐵 / 𝑥]𝜓))
31, 2syl 14 1 (𝜑 → ([𝐴 / 𝑥]𝜓[𝐵 / 𝑥]𝜓))
 Colors of variables: wff set class Syntax hints:   → wi 4   ↔ wb 104   = wceq 1290  [wsbc 2843 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1382  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-4 1446  ax-17 1465  ax-ial 1473  ax-ext 2071 This theorem depends on definitions:  df-bi 116  df-cleq 2082  df-clel 2085  df-sbc 2844 This theorem is referenced by:  sbceq1dd  2849  rexrnmpt  5458  findcard2  6661  findcard2s  6662  ac6sfi  6670  nn1suc  8504  uzind4s  9141  uzind4s2  9142  fzrevral  9582  fzshftral  9585  cjth  10343  prmind2  11443  bj-bdfindes  12148  bj-findes  12180
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