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Theorem bj-1upleq 32180
 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 32169 . 2 (𝐴 = 𝐵 → ({∅} × tag 𝐴) = ({∅} × tag 𝐵))
2 df-bj-1upl 32179 . 2 𝐴⦆ = ({∅} × tag 𝐴)
3 df-bj-1upl 32179 . 2 𝐵⦆ = ({∅} × tag 𝐵)
41, 2, 33eqtr4g 2669 1 (𝐴 = 𝐵 → ⦅𝐴⦆ = ⦅𝐵⦆)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1475  ∅c0 3874  {csn 4125   × cxp 5036  tag bj-ctag 32155  ⦅bj-c1upl 32178 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-rex 2902  df-v 3175  df-un 3545  df-opab 4644  df-xp 5044  df-bj-sngl 32147  df-bj-tag 32156  df-bj-1upl 32179 This theorem is referenced by:  bj-1uplth  32188  bj-2upleq  32193
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