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Theorem bj-1upleq 35283
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 35272 . 2 (𝐴 = 𝐵 → ({∅} × tag 𝐴) = ({∅} × tag 𝐵))
2 df-bj-1upl 35282 . 2 𝐴⦆ = ({∅} × tag 𝐴)
3 df-bj-1upl 35282 . 2 𝐵⦆ = ({∅} × tag 𝐵)
41, 2, 33eqtr4g 2801 1 (𝐴 = 𝐵 → ⦅𝐴⦆ = ⦅𝐵⦆)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1540  c0 4269  {csn 4573   × cxp 5618  tag bj-ctag 35258  bj-c1upl 35281
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2707
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-tru 1543  df-ex 1781  df-sb 2067  df-clab 2714  df-cleq 2728  df-clel 2814  df-ral 3062  df-rex 3071  df-v 3443  df-un 3903  df-opab 5155  df-xp 5626  df-bj-sngl 35250  df-bj-tag 35259  df-bj-1upl 35282
This theorem is referenced by:  bj-1uplth  35291  bj-2upleq  35296
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