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Theorem nfsbc1 2858
Description: Bound-variable hypothesis builder for class substitution. (Contributed by Mario Carneiro, 12-Oct-2016.)
Hypothesis
Ref Expression
nfsbc1.1  |-  F/_ x A
Assertion
Ref Expression
nfsbc1  |-  F/ x [. A  /  x ]. ph

Proof of Theorem nfsbc1
StepHypRef Expression
1 nfsbc1.1 . . . 4  |-  F/_ x A
21a1i 9 . . 3  |-  ( T. 
->  F/_ x A )
32nfsbc1d 2857 . 2  |-  ( T. 
->  F/ x [. A  /  x ]. ph )
43mptru 1299 1  |-  F/ x [. A  /  x ]. ph
Colors of variables: wff set class
Syntax hints:   T. wtru 1291   F/wnf 1395   F/_wnfc 2216   [.wsbc 2841
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-11 1443  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071
This theorem depends on definitions:  df-bi 116  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-sbc 2842
This theorem is referenced by:  nfsbc1v  2859  riotass2  5648  riotass  5649  bj-intabssel  11955
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