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Theorem nfcsb 2884
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 1355 . . 3 𝑦
2 nfcsb.1 . . . 4 𝑥𝐴
32a1i 9 . . 3 (⊤ → 𝑥𝐴)
4 nfcsb.2 . . . 4 𝑥𝐵
54a1i 9 . . 3 (⊤ → 𝑥𝐵)
61, 3, 5nfcsbd 2883 . 2 (⊤ → 𝑥𝐴 / 𝑦𝐵)
76trud 1252 1 𝑥𝐴 / 𝑦𝐵
Colors of variables: wff set class
Syntax hints:  wtru 1244  wnfc 2165  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-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  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-nfc 2167  df-sbc 2765  df-csb 2853
This theorem is referenced by:  cbvralcsf  2908  cbvrexcsf  2909  cbvreucsf  2910  cbvrabcsf  2911  fmptcof  5331  mpt2mptsx  5823  dmmpt2ssx  5825  fmpt2x  5826  fmpt2co  5837  dfmpt2  5844  nfsum  9876
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