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Theorem nfsbc1 3009
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 3008 . 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 1531   F/_wnfc 2406   [.wsbc 2991
This theorem is referenced by:  nfsbc1v  3010  riotass2  6332  riotass  6333  bnj873  28956
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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