Theorem bj-1upleq 38127

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 38116	. 2 ⊢ (𝐴 = 𝐵 → ({∅} × tag 𝐴) = ({∅} × tag 𝐵))
2		df-bj-1upl 38126	. 2 ⊢ ⦅𝐴⦆ = ({∅} × tag 𝐴)
3		df-bj-1upl 38126	. 2 ⊢ ⦅𝐵⦆ = ({∅} × tag 𝐵)
4	1, 2, 3	3eqtr4g 2823	1 ⊢ (𝐴 = 𝐵 → ⦅𝐴⦆ = ⦅𝐵⦆)

This proof depends on syntax axioms:   → wi 4   = wceq 1570  ∅c0 4281  {csn 4588   × cxp 5656  tag bj-ctag 38102  ⦅bj-c1upl 38125

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-rex 3091  df-v 3456  df-un 4154  df-opab 5174  df-xp 5664  df-bj-sngl 38094  df-bj-tag 38103  df-bj-1upl 38126

This theorem is used by:  bj-1uplth  38135  bj-2upleq  38140