Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-1upleq Structured version   Visualization version   GIF version

Theorem bj-1upleq 36387
Description: Substitution property for ⦅ − ⦆. (Contributed by BJ, 6-Apr-2019.)
Assertion
Ref Expression
bj-1upleq (𝐴 = 𝐵 → ⦅𝐴⦆ = ⦅𝐵⦆)

Proof of Theorem bj-1upleq
StepHypRef Expression
1 bj-xtageq 36376 . 2 (𝐴 = 𝐵 → ({∅} × tag 𝐴) = ({∅} × tag 𝐵))
2 df-bj-1upl 36386 . 2 𝐴⦆ = ({∅} × tag 𝐴)
3 df-bj-1upl 36386 . 2 𝐵⦆ = ({∅} × tag 𝐵)
41, 2, 33eqtr4g 2791 1 (𝐴 = 𝐵 → ⦅𝐴⦆ = ⦅𝐵⦆)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1533  c0 4317  {csn 4623   × cxp 5667  tag bj-ctag 36362  bj-c1upl 36385
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2697
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2704  df-cleq 2718  df-clel 2804  df-rex 3065  df-v 3470  df-un 3948  df-opab 5204  df-xp 5675  df-bj-sngl 36354  df-bj-tag 36363  df-bj-1upl 36386
This theorem is referenced by:  bj-1uplth  36395  bj-2upleq  36400
  Copyright terms: Public domain W3C validator