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Theorem bj-1upleq 33112
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 33101 . 2 (𝐴 = 𝐵 → ({∅} × tag 𝐴) = ({∅} × tag 𝐵))
2 df-bj-1upl 33111 . 2 𝐴⦆ = ({∅} × tag 𝐴)
3 df-bj-1upl 33111 . 2 𝐵⦆ = ({∅} × tag 𝐵)
41, 2, 33eqtr4g 2710 1 (𝐴 = 𝐵 → ⦅𝐴⦆ = ⦅𝐵⦆)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1523  c0 3948  {csn 4210   × cxp 5141  tag bj-ctag 33087  bj-c1upl 33110
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-rex 2947  df-v 3233  df-un 3612  df-opab 4746  df-xp 5149  df-bj-sngl 33079  df-bj-tag 33088  df-bj-1upl 33111
This theorem is referenced by:  bj-1uplth  33120  bj-2upleq  33125
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