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Theorem bj-1upleq 34208
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 34197 . 2 (𝐴 = 𝐵 → ({∅} × tag 𝐴) = ({∅} × tag 𝐵))
2 df-bj-1upl 34207 . 2 𝐴⦆ = ({∅} × tag 𝐴)
3 df-bj-1upl 34207 . 2 𝐵⦆ = ({∅} × tag 𝐵)
41, 2, 33eqtr4g 2878 1 (𝐴 = 𝐵 → ⦅𝐴⦆ = ⦅𝐵⦆)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1528  c0 4288  {csn 4557   × cxp 5546  tag bj-ctag 34183  bj-c1upl 34206
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-nfc 2960  df-rex 3141  df-v 3494  df-un 3938  df-opab 5120  df-xp 5554  df-bj-sngl 34175  df-bj-tag 34184  df-bj-1upl 34207
This theorem is referenced by:  bj-1uplth  34216  bj-2upleq  34221
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