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Theorem nfsbc1 3318
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 3317 . 2  |-  ( T. 
->  F/ x [. A  /  x ]. ph )
43trud 1446 1  |-  F/ x [. A  /  x ]. ph
Colors of variables: wff setvar class
Syntax hints:   T. wtru 1438   F/wnf 1663   F/_wnfc 2570   [.wsbc 3299
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-10 1887  ax-11 1892  ax-12 1905  ax-13 2053  ax-ext 2400
This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2572  df-sbc 3300
This theorem is referenced by:  nfsbc1v  3319  riotass2  6289  riotass  6290  uzwo4  37251
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