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Theorem nfcsb 2950
Description: Bound-variable hypothesis builder for substitution into a class. (Contributed by Mario Carneiro, 12-Oct-2016.)
Hypotheses
Ref Expression
nfcsb.1 𝑥𝐴
nfcsb.2 𝑥𝐵
Assertion
Ref Expression
nfcsb 𝑥𝐴 / 𝑦𝐵

Proof of Theorem nfcsb
StepHypRef Expression
1 nftru 1396 . . 3 𝑦
2 nfcsb.1 . . . 4 𝑥𝐴
32a1i 9 . . 3 (⊤ → 𝑥𝐴)
4 nfcsb.2 . . . 4 𝑥𝐵
54a1i 9 . . 3 (⊤ → 𝑥𝐵)
61, 3, 5nfcsbd 2949 . 2 (⊤ → 𝑥𝐴 / 𝑦𝐵)
76trud 1294 1 𝑥𝐴 / 𝑦𝐵
Colors of variables: wff set class
Syntax hints:  wtru 1286  wnfc 2210  csb 2918
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-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-sbc 2826  df-csb 2919
This theorem is referenced by:  cbvralcsf  2974  cbvrexcsf  2975  cbvreucsf  2976  cbvrabcsf  2977  fmptcof  5385  mpt2mptsx  5876  dmmpt2ssx  5878  fmpt2x  5879  fmpt2co  5890  dfmpt2  5897  f1od2  5909  nfsum  10420
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