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Theorem nfsbc1 3022
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 10 . . 3  |-  (  T. 
->  F/_ x A )
32nfsbc1d 3021 . 2  |-  (  T. 
->  F/ x [. A  /  x ]. ph )
43trud 1314 1  |-  F/ x [. A  /  x ]. ph
Colors of variables: wff set class
Syntax hints:    T. wtru 1307   F/wnf 1534   F/_wnfc 2419   [.wsbc 3004
This theorem is referenced by:  nfsbc1v  3023  riotass2  6348  riotass  6349  bnj873  29272
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-sbc 3005
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