Theorem bj-1upleq 34314

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 34303	. 2 ⊢ (𝐴 = 𝐵 → ({∅} × tag 𝐴) = ({∅} × tag 𝐵))
2		df-bj-1upl 34313	. 2 ⊢ ⦅𝐴⦆ = ({∅} × tag 𝐴)
3		df-bj-1upl 34313	. 2 ⊢ ⦅𝐵⦆ = ({∅} × tag 𝐵)
4	1, 2, 3	3eqtr4g 2881	1 ⊢ (𝐴 = 𝐵 → ⦅𝐴⦆ = ⦅𝐵⦆)

Syntax hints:   → wi 4   = wceq 1537  ∅c0 4291  {csn 4567   × cxp 5553  tag bj-ctag 34289  ⦅bj-c1upl 34312

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 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2177  ax-ext 2793

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1540  df-ex 1781  df-nf 1785  df-sb 2070  df-clab 2800  df-cleq 2814  df-clel 2893  df-nfc 2963  df-rex 3144  df-v 3496  df-un 3941  df-opab 5129  df-xp 5561  df-bj-sngl 34281  df-bj-tag 34290  df-bj-1upl 34313

This theorem is referenced by:  bj-1uplth  34322  bj-2upleq  34327