Theorem bj-1upleq 37746

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 37735	. 2 ⊢ (𝐴 = 𝐵 → ({∅} × tag 𝐴) = ({∅} × tag 𝐵))
2		df-bj-1upl 37745	. 2 ⊢ ⦅𝐴⦆ = ({∅} × tag 𝐴)
3		df-bj-1upl 37745	. 2 ⊢ ⦅𝐵⦆ = ({∅} × tag 𝐵)
4	1, 2, 3	3eqtr4g 2820	1 ⊢ (𝐴 = 𝐵 → ⦅𝐴⦆ = ⦅𝐵⦆)

This proof depends on syntax axioms:   → wi 4   = wceq 1570  ∅c0 4279  {csn 4584   × cxp 5653  tag bj-ctag 37721  ⦅bj-c1upl 37744

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 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2739  df-cleq 2752  df-clel 2835  df-rex 3087  df-v 3452  df-un 3904  df-opab 5168  df-xp 5661  df-bj-sngl 37713  df-bj-tag 37722  df-bj-1upl 37745

This theorem is used by:  bj-1uplth  37754  bj-2upleq  37759