ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  nfsbc1 GIF version

Theorem nfsbc1 2954
Description: Bound-variable hypothesis builder for class substitution. (Contributed by Mario Carneiro, 12-Oct-2016.)
Hypothesis
Ref Expression
nfsbc1.1 𝑥𝐴
Assertion
Ref Expression
nfsbc1 𝑥[𝐴 / 𝑥]𝜑

Proof of Theorem nfsbc1
StepHypRef Expression
1 nfsbc1.1 . . . 4 𝑥𝐴
21a1i 9 . . 3 (⊤ → 𝑥𝐴)
32nfsbc1d 2953 . 2 (⊤ → Ⅎ𝑥[𝐴 / 𝑥]𝜑)
43mptru 1344 1 𝑥[𝐴 / 𝑥]𝜑
Colors of variables: wff set class
Syntax hints:  wtru 1336  wnf 1440  wnfc 2286  [wsbc 2937
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-11 1486  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139
This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-sbc 2938
This theorem is referenced by:  nfsbc1v  2955  riotass2  5807  riotass  5808  bj-intabssel  13405
  Copyright terms: Public domain W3C validator