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Theorem csbeq2i 2876
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 2875 . 2 (⊤ → 𝐴 / 𝑥𝐵 = 𝐴 / 𝑥𝐶)
43trud 1252 1 𝐴 / 𝑥𝐵 = 𝐴 / 𝑥𝐶
Colors of variables: wff set class
Syntax hints:   = wceq 1243  wtru 1244  csb 2852
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-sbc 2765  df-csb 2853
This theorem is referenced by:  csbvarg  2877  csbnest1g  2901  csbsng  3431  csbunig  3588  csbxpg  4421  csbcnvg  4519  csbdmg  4529  csbresg  4615  csbrng  4782  csbfv12g  5209  csbnegg  7207
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