Theorem bj-1upleq 37484

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 37473	. 2 ⊢ (𝐴 = 𝐵 → ({∅} × tag 𝐴) = ({∅} × tag 𝐵))
2		df-bj-1upl 37483	. 2 ⊢ ⦅𝐴⦆ = ({∅} × tag 𝐴)
3		df-bj-1upl 37483	. 2 ⊢ ⦅𝐵⦆ = ({∅} × tag 𝐵)
4	1, 2, 3	3eqtr4g 2822	1 ⊢ (𝐴 = 𝐵 → ⦅𝐴⦆ = ⦅𝐵⦆)

Syntax hints:   → wi 4   = wceq 1560  ∅c0 4285  {csn 4582   × cxp 5645  tag bj-ctag 37459  ⦅bj-c1upl 37482

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1815  ax-4 1829  ax-5 1930  ax-6 1987  ax-7 2028  ax-8 2144  ax-9 2152  ax-ext 2734

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-tru 1563  df-ex 1800  df-sb 2091  df-clab 2741  df-cleq 2754  df-clel 2837  df-rex 3087  df-v 3456  df-un 3909  df-opab 5163  df-xp 5653  df-bj-sngl 37451  df-bj-tag 37460  df-bj-1upl 37483

This theorem is referenced by:  bj-1uplth  37492  bj-2upleq  37497