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Theorem sbceq1d 2914
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 2911 . 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 1331  [wsbc 2909
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-17 1506  ax-ial 1514  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-cleq 2132  df-clel 2135  df-sbc 2910
This theorem is referenced by:  sbceq1dd  2915  rexrnmpt  5563  findcard2  6783  findcard2s  6784  ac6sfi  6792  nn1suc  8753  uzind4s  9399  uzind4s2  9400  fzrevral  9899  fzshftral  9902  cjth  10632  prmind2  11814  bj-bdfindes  13254  bj-findes  13286
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