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Theorem nfsbc1 3350
Description: Bound-variable hypothesis builder for class substitution. (Contributed by NM, 5-Aug-1993.) (Revised 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 3349 . 2  |-  ( T. 
->  F/ x [. A  /  x ]. ph )
43trud 1388 1  |-  F/ x [. A  /  x ]. ph
Colors of variables: wff setvar class
Syntax hints:   T. wtru 1380   F/wnf 1599   F/_wnfc 2615   [.wsbc 3331
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-sbc 3332
This theorem is referenced by:  nfsbc1v  3351  riotass2  6270  riotass  6271  ovmpt3rabdm  6517
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