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Theorem nfsbc1 3171
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 3170 . 2  |-  (  T. 
->  F/ x [. A  /  x ]. ph )
43trud 1332 1  |-  F/ x [. A  /  x ]. ph
Colors of variables: wff set class
Syntax hints:    T. wtru 1325   F/wnf 1553   F/_wnfc 2558   [.wsbc 3153
This theorem is referenced by:  nfsbc1v  3172  riotass2  6569  riotass  6570
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-sbc 3154
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