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Theorem nfsbc1 3274
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 3273 . 2  |-  ( T. 
->  F/ x [. A  /  x ]. ph )
43trud 1461 1  |-  F/ x [. A  /  x ]. ph
Colors of variables: wff setvar class
Syntax hints:   T. wtru 1453   F/wnf 1675   F/_wnfc 2599   [.wsbc 3255
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451
This theorem depends on definitions:  df-bi 190  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-sbc 3256
This theorem is referenced by:  nfsbc1v  3275  riotass2  6296  riotass  6297  uzwo4  37451
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