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Theorem csbeq2dv 2945
Description: Formula-building deduction rule for class substitution. (Contributed by NM, 10-Nov-2005.) (Revised by Mario Carneiro, 1-Sep-2015.)
Hypothesis
Ref Expression
csbeq2dv.1 (𝜑𝐵 = 𝐶)
Assertion
Ref Expression
csbeq2dv (𝜑𝐴 / 𝑥𝐵 = 𝐴 / 𝑥𝐶)
Distinct variable group:   𝜑,𝑥
Allowed substitution hints:   𝐴(𝑥)   𝐵(𝑥)   𝐶(𝑥)

Proof of Theorem csbeq2dv
StepHypRef Expression
1 nfv 1464 . 2 𝑥𝜑
2 csbeq2dv.1 . 2 (𝜑𝐵 = 𝐶)
31, 2csbeq2d 2944 1 (𝜑𝐴 / 𝑥𝐵 = 𝐴 / 𝑥𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1287  csb 2922
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-11 1440  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-sbc 2830  df-csb 2923
This theorem is referenced by:  csbeq2i  2946  mpt2mptsx  5918  dmmpt2ssx  5920  fmpt2x  5921  fmpt2co  5932
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