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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  |-  F/_ x A
nfsbc.2  |-  F/ x ph
Assertion
Ref Expression
nfsbc  |-  F/ x [. A  /  y ]. ph

Proof of Theorem nfsbc
StepHypRef Expression
1 nftru 1396 . . 3  |-  F/ y T.
2 nfsbc.1 . . . 4  |-  F/_ x A
32a1i 9 . . 3  |-  ( T. 
->  F/_ x A )
4 nfsbc.2 . . . 4  |-  F/ x ph
54a1i 9 . . 3  |-  ( T. 
->  F/ x ph )
61, 3, 5nfsbcd 2835 . 2  |-  ( T. 
->  F/ x [. A  /  y ]. ph )
76trud 1294 1  |-  F/ x [. A  /  y ]. ph
Colors of variables: wff set class
Syntax hints:   T. wtru 1286   F/wnf 1390   F/_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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