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Theorem csbeq2i 3058
 Description: Formula-building inference 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 3057 . 2 (⊤ → 𝐴 / 𝑥𝐵 = 𝐴 / 𝑥𝐶)
43mptru 1344 1 𝐴 / 𝑥𝐵 = 𝐴 / 𝑥𝐶
 Colors of variables: wff set class Syntax hints:   = wceq 1335  ⊤wtru 1336  ⦋csb 3031 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 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-11 1486  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-sbc 2938  df-csb 3032 This theorem is referenced by:  csbvarg  3059  csbnest1g  3086  csbsng  3620  csbunig  3780  csbxpg  4664  csbcnvg  4767  csbdmg  4777  csbresg  4866  csbrng  5044  csbfv12g  5501  csbnegg  8056  iseqf1olemjpcl  10376  iseqf1olemqpcl  10377  iseqf1olemfvp  10378  seq3f1olemqsum  10381
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