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Theorem csbeq2dv 3083
Description: Formula-building deduction 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 1528 . 2 𝑥𝜑
2 csbeq2dv.1 . 2 (𝜑𝐵 = 𝐶)
31, 2csbeq2d 3082 1 (𝜑𝐴 / 𝑥𝐵 = 𝐴 / 𝑥𝐶)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1353  csb 3057
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-sbc 2963  df-csb 3058
This theorem is referenced by:  csbeq2i  3084  mpomptsx  6195  dmmpossx  6197  fmpox  6198  fmpoco  6214  fisumcom2  11439  fprodcom2fi  11627  fsumcncntop  13927
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