MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  nfsbc1 Structured version   Unicode version

Theorem nfsbc1 3298
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 3297 . 2  |-  ( T. 
->  F/ x [. A  /  x ]. ph )
43trud 1416 1  |-  F/ x [. A  /  x ]. ph
Colors of variables: wff setvar class
Syntax hints:   T. wtru 1408   F/wnf 1639   F/_wnfc 2552   [.wsbc 3279
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1641  ax-4 1654  ax-5 1727  ax-6 1773  ax-7 1816  ax-10 1863  ax-11 1868  ax-12 1880  ax-13 2028  ax-ext 2382
This theorem depends on definitions:  df-bi 187  df-an 371  df-tru 1410  df-ex 1636  df-nf 1640  df-sb 1766  df-clab 2390  df-cleq 2396  df-clel 2399  df-nfc 2554  df-sbc 3280
This theorem is referenced by:  nfsbc1v  3299  riotass2  6268  riotass  6269
  Copyright terms: Public domain W3C validator