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Theorem bj-1upleq 37001
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 36990 . 2 (𝐴 = 𝐵 → ({∅} × tag 𝐴) = ({∅} × tag 𝐵))
2 df-bj-1upl 37000 . 2 𝐴⦆ = ({∅} × tag 𝐴)
3 df-bj-1upl 37000 . 2 𝐵⦆ = ({∅} × tag 𝐵)
41, 2, 33eqtr4g 2801 1 (𝐴 = 𝐵 → ⦅𝐴⦆ = ⦅𝐵⦆)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1539  c0 4332  {csn 4625   × cxp 5682  tag bj-ctag 36976  bj-c1upl 36999
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1542  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-rex 3070  df-v 3481  df-un 3955  df-opab 5205  df-xp 5690  df-bj-sngl 36968  df-bj-tag 36977  df-bj-1upl 37000
This theorem is referenced by:  bj-1uplth  37009  bj-2upleq  37014
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