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Theorem sbceq1d 2789
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 2786 . 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 102   = wceq 1257  [wsbc 2784
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 1350  ax-gen 1352  ax-ie1 1396  ax-ie2 1397  ax-4 1414  ax-17 1433  ax-ial 1441  ax-ext 2036
This theorem depends on definitions:  df-bi 114  df-cleq 2047  df-clel 2050  df-sbc 2785
This theorem is referenced by:  sbceq1dd  2790  rexrnmpt  5335  findcard2  6374  findcard2s  6375  ac6sfi  6380  nn1suc  7979  uzind4s  8599  uzind4s2  8600  fzrevral  9039  fzshftral  9042  cjth  9638  bj-bdfindes  10404  bj-findes  10436
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