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Theorem nfsbc 2836
 Description: Bound-variable hypothesis builder for class substitution. (Contributed by NM, 7-Sep-2014.) (Revised by Mario Carneiro, 12-Oct-2016.)
Hypotheses
Ref Expression
nfsbc.1
nfsbc.2
Assertion
Ref Expression
nfsbc

Proof of Theorem nfsbc
StepHypRef Expression
1 nftru 1396 . . 3
2 nfsbc.1 . . . 4
32a1i 9 . . 3
4 nfsbc.2 . . . 4
54a1i 9 . . 3
61, 3, 5nfsbcd 2835 . 2
76trud 1294 1
 Colors of variables: wff set class Syntax hints:   wtru 1286  wnf 1390  wnfc 2207  wsbc 2816 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 2064 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-sbc 2817 This theorem is referenced by:  cbvralcsf  2965  cbvrexcsf  2966  opelopabf  4031  ralrnmpt  5335  rexrnmpt  5336  dfopab2  5840  dfoprab3s  5841  mpt2xopoveq  5883
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