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Theorem bj-1upleq 34952
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 34941 . 2 (𝐴 = 𝐵 → ({∅} × tag 𝐴) = ({∅} × tag 𝐵))
2 df-bj-1upl 34951 . 2 𝐴⦆ = ({∅} × tag 𝐴)
3 df-bj-1upl 34951 . 2 𝐵⦆ = ({∅} × tag 𝐵)
41, 2, 33eqtr4g 2804 1 (𝐴 = 𝐵 → ⦅𝐴⦆ = ⦅𝐵⦆)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1543  c0 4251  {csn 4555   × cxp 5563  tag bj-ctag 34927  bj-c1upl 34950
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2113  ax-9 2121  ax-ext 2709
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 848  df-tru 1546  df-ex 1788  df-sb 2072  df-clab 2716  df-cleq 2730  df-clel 2817  df-ral 3067  df-rex 3068  df-v 3422  df-un 3885  df-opab 5130  df-xp 5571  df-bj-sngl 34919  df-bj-tag 34928  df-bj-1upl 34951
This theorem is referenced by:  bj-1uplth  34960  bj-2upleq  34965
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