ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  sbceq1d Structured version   GIF version

Theorem sbceq1d 2763
Description: Equality theorem for class substitution. (Contributed by Mario Carneiro, 9-Feb-2017.) (Revised by NM, 30-Jun-2018.)
Hypothesis
Ref Expression
sbceq1d.1 (φA = B)
Assertion
Ref Expression
sbceq1d (φ → ([A / x]ψ[B / x]ψ))

Proof of Theorem sbceq1d
StepHypRef Expression
1 sbceq1d.1 . 2 (φA = B)
2 dfsbcq 2760 . 2 (A = B → ([A / x]ψ[B / x]ψ))
31, 2syl 14 1 (φ → ([A / x]ψ[B / x]ψ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98   = wceq 1242  [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-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-cleq 2030  df-clel 2033  df-sbc 2759
This theorem is referenced by:  sbceq1dd  2764  rexrnmpt  5253  nn1suc  7714  uzind4s  8309  uzind4s2  8310  fzrevral  8737  fzshftral  8740  cjth  9074  bj-bdfindes  9409  bj-findes  9441
  Copyright terms: Public domain W3C validator