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Theorem csbeq2i 2945
Description: Formula-building inference rule for class substitution. (Contributed by NM, 10-Nov-2005.) (Revised by Mario Carneiro, 1-Sep-2015.)
Hypothesis
Ref Expression
csbeq2i.1 𝐵 = 𝐶
Assertion
Ref Expression
csbeq2i 𝐴 / 𝑥𝐵 = 𝐴 / 𝑥𝐶

Proof of Theorem csbeq2i
StepHypRef Expression
1 csbeq2i.1 . . . 4 𝐵 = 𝐶
21a1i 9 . . 3 (⊤ → 𝐵 = 𝐶)
32csbeq2dv 2944 . 2 (⊤ → 𝐴 / 𝑥𝐵 = 𝐴 / 𝑥𝐶)
43trud 1296 1 𝐴 / 𝑥𝐵 = 𝐴 / 𝑥𝐶
Colors of variables: wff set class
Syntax hints:   = wceq 1287  wtru 1288  csb 2921
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 2829  df-csb 2922
This theorem is referenced by:  csbvarg  2946  csbnest1g  2970  csbsng  3480  csbunig  3638  csbxpg  4480  csbcnvg  4581  csbdmg  4591  csbresg  4677  csbrng  4849  csbfv12g  5288  csbnegg  7601
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