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

Theorem sbcbii 3014
Description: Formula-building inference for class substitution. (Contributed by NM, 11-Nov-2005.)
Hypothesis
Ref Expression
sbcbii.1 (𝜑𝜓)
Assertion
Ref Expression
sbcbii ([𝐴 / 𝑥]𝜑[𝐴 / 𝑥]𝜓)

Proof of Theorem sbcbii
StepHypRef Expression
1 sbcbii.1 . . . 4 (𝜑𝜓)
21a1i 9 . . 3 (⊤ → (𝜑𝜓))
32sbcbidv 3013 . 2 (⊤ → ([𝐴 / 𝑥]𝜑[𝐴 / 𝑥]𝜓))
43mptru 1357 1 ([𝐴 / 𝑥]𝜑[𝐴 / 𝑥]𝜓)
Colors of variables: wff set class
Syntax hints:  wb 104  wtru 1349  [wsbc 2955
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 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-11 1499  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-sbc 2956
This theorem is referenced by:  eqsbc2  3015  sbc3an  3016  sbccomlem  3029  sbccom  3030  sbcabel  3036  csbco  3059  csbcow  3060  sbcnel12g  3066  sbcne12g  3067  sbccsbg  3078  sbccsb2g  3079  csbnestgf  3101  csbabg  3110  sbcssg  3524  sbcrel  4697  difopab  4744  sbcfung  5222  f1od2  6214  mpoxopovel  6220  bezoutlemnewy  11951  bezoutlemstep  11952  bezoutlemmain  11953
  Copyright terms: Public domain W3C validator