Theorem bj-1upleq

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

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

Proof

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