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Theorem nfsbc 3012
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 1541 . . 3  |-  F/ y  T.
2 nfsbc.1 . . . 4  |-  F/_ x A
32a1i 10 . . 3  |-  (  T. 
->  F/_ x A )
4 nfsbc.2 . . . 4  |-  F/ x ph
54a1i 10 . . 3  |-  (  T. 
->  F/ x ph )
61, 3, 5nfsbcd 3011 . 2  |-  (  T. 
->  F/ x [. A  /  y ]. ph )
76trud 1314 1  |-  F/ x [. A  /  y ]. ph
Colors of variables: wff set class
Syntax hints:    T. wtru 1307   F/wnf 1531   F/_wnfc 2406   [.wsbc 2991
This theorem is referenced by:  cbvralcsf  3143  opelopabf  4289  ralrnmpt  5669  dfopab2  6174  dfoprab3s  6175  elmptrab  17522  indexa  26412  sdclem1  26453  sbccomieg  26870  rexrabdioph  26875  mpt2xopoveq  28085  bnj1445  29074  bnj1446  29075  bnj1467  29084
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-sbc 2992
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