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Theorem nfcsb 3037
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 1442 . . 3 𝑦
2 nfcsb.1 . . . 4 𝑥𝐴
32a1i 9 . . 3 (⊤ → 𝑥𝐴)
4 nfcsb.2 . . . 4 𝑥𝐵
54a1i 9 . . 3 (⊤ → 𝑥𝐵)
61, 3, 5nfcsbd 3036 . 2 (⊤ → 𝑥𝐴 / 𝑦𝐵)
76mptru 1340 1 𝑥𝐴 / 𝑦𝐵
Colors of variables: wff set class
Syntax hints:  wtru 1332  wnfc 2268  csb 3003
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-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-sbc 2910  df-csb 3004
This theorem is referenced by:  cbvralcsf  3062  cbvrexcsf  3063  cbvreucsf  3064  cbvrabcsf  3065  elfvmptrab1  5515  fmptcof  5587  mpomptsx  6095  dmmpossx  6097  fmpox  6098  fmpoco  6113  dfmpo  6120  f1od2  6132  nfsum  11133  fsum2dlemstep  11210  fisumcom2  11214  nfcprod  11331  fsumcncntop  12734
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