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Theorem nfsbc1 3122
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 11 . . 3  |-  (  T. 
->  F/_ x A )
32nfsbc1d 3121 . 2  |-  (  T. 
->  F/ x [. A  /  x ]. ph )
43trud 1329 1  |-  F/ x [. A  /  x ]. ph
Colors of variables: wff set class
Syntax hints:    T. wtru 1322   F/wnf 1550   F/_wnfc 2510   [.wsbc 3104
This theorem is referenced by:  nfsbc1v  3123  riotass2  6513  riotass  6514
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2374  df-cleq 2380  df-clel 2383  df-nfc 2512  df-sbc 3105
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