Theorem bj-1uplth

Description: The characteristic property of monuples. Note that this holds without sethood hypotheses. (Contributed by BJ, 6-Apr-2019)

	Ref	Expression
Assertion	bj-1uplth	|- ( (| A |) = (| B |) <-> A = B )

Proof

Step	Hyp	Ref	Expression
1		bj-pr1eq	|- ( (| A |) = (| B |) -> pr1 (| A |) = pr1 (| B |) )
2		bj-pr11val	|- pr1 (| A |) = A
3		bj-pr11val	|- pr1 (| B |) = B
4	1 2 3	3eqtr3g	|- ( (| A |) = (| B |) -> A = B )
5		bj-1upleq	|- ( A = B -> (| A |) = (| B |) )
6	4 5	impbii	|- ( (| A |) = (| B |) <-> A = B )