Metamath Proof Explorer


Theorem r2ex

Description: Double restricted existential quantification. (Contributed by NM, 11-Nov-1995) Reduce dependencies on axioms. (Revised by Wolf Lammen, 10-Jan-2020)

Ref Expression
Assertion r2ex xAyBφxyxAyBφ

Proof

Step Hyp Ref Expression
1 r2al xAyB¬φxyxAyB¬φ
2 1 r2exlem xAyBφxyxAyBφ