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

Theorem sbcbii 2812
Description: Formula-building inference rule 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 2811 . 2 ( ⊤ → ([A / x]φ[A / x]ψ))
43trud 1251 1 ([A / x]φ[A / x]ψ)
Colors of variables: wff set class
Syntax hints:  wb 98  wtru 1243  [wsbc 2758
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-sbc 2759
This theorem is referenced by:  eqsbc3r  2813  sbccomlem  2826  sbccom  2827  sbcabel  2833  csbco  2855  sbcnel12g  2861  sbcne12g  2862  sbccsbg  2872  sbccsb2g  2873  csbnestgf  2892  csbabg  2901  sbcssg  3324  sbcrel  4369  difopab  4412  sbcfung  4868  mpt2xopovel  5797
  Copyright terms: Public domain W3C validator