Theorem bj-1upleq 36535

Description: Substitution property for ⦅ − ⦆. (Contributed by BJ, 6-Apr-2019.)

Assertion

Ref	Expression
bj-1upleq	⊢ (𝐴 = 𝐵 → ⦅𝐴⦆ = ⦅𝐵⦆)

Proof of Theorem bj-1upleq

Step	Hyp	Ref	Expression
1		bj-xtageq 36524	. 2 ⊢ (𝐴 = 𝐵 → ({∅} × tag 𝐴) = ({∅} × tag 𝐵))
2		df-bj-1upl 36534	. 2 ⊢ ⦅𝐴⦆ = ({∅} × tag 𝐴)
3		df-bj-1upl 36534	. 2 ⊢ ⦅𝐵⦆ = ({∅} × tag 𝐵)
4	1, 2, 3	3eqtr4g 2790	1 ⊢ (𝐴 = 𝐵 → ⦅𝐴⦆ = ⦅𝐵⦆)

Syntax hints:   → wi 4   = wceq 1533  ∅c0 4318  {csn 4624   × cxp 5670  tag bj-ctag 36510  ⦅bj-c1upl 36533

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2696

This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2703  df-cleq 2717  df-clel 2802  df-rex 3061  df-v 3465  df-un 3944  df-opab 5206  df-xp 5678  df-bj-sngl 36502  df-bj-tag 36511  df-bj-1upl 36534

This theorem is referenced by:  bj-1uplth  36543  bj-2upleq  36548