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Theorem csbeq2i 2995
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 2994 . 2 (⊤ → 𝐴 / 𝑥𝐵 = 𝐴 / 𝑥𝐶)
43mptru 1323 1 𝐴 / 𝑥𝐵 = 𝐴 / 𝑥𝐶
Colors of variables: wff set class
Syntax hints:   = wceq 1314  wtru 1315  csb 2971
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-11 1467  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-sbc 2879  df-csb 2972
This theorem is referenced by:  csbvarg  2996  csbnest1g  3021  csbsng  3550  csbunig  3710  csbxpg  4580  csbcnvg  4683  csbdmg  4693  csbresg  4780  csbrng  4958  csbfv12g  5411  csbnegg  7883  iseqf1olemjpcl  10161  iseqf1olemqpcl  10162  iseqf1olemfvp  10163  seq3f1olemqsum  10166
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