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Theorem nfcsb 2878
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 1352 . . 3 y
2 nfcsb.1 . . . 4 xA
32a1i 9 . . 3 ( ⊤ → xA)
4 nfcsb.2 . . . 4 xB
54a1i 9 . . 3 ( ⊤ → xB)
61, 3, 5nfcsbd 2877 . 2 ( ⊤ → xA / yB)
76trud 1251 1 xA / yB
Colors of variables: wff set class
Syntax hints:  wtru 1243  wnfc 2162  csb 2846
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-sbc 2759  df-csb 2847
This theorem is referenced by:  cbvralcsf  2902  cbvrexcsf  2903  cbvreucsf  2904  cbvrabcsf  2905  fmptcof  5274  mpt2mptsx  5765  dmmpt2ssx  5767  fmpt2x  5768  fmpt2co  5779  dfmpt2  5786
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