Metamath Proof Explorer


Theorem preleq

Description: Equality of two unordered pairs when one member of each pair contains the other member. (Contributed by NM, 16-Oct-1996) (Revised by AV, 15-Jun-2022)

Ref Expression
Hypothesis preleq.b B V
Assertion preleq A B C D A B = C D A = C B = D

Proof

Step Hyp Ref Expression
1 preleq.b B V
2 preleqg A B B V C D A B = C D A = C B = D
3 1 2 mp3anl2 A B C D A B = C D A = C B = D