Metamath Proof Explorer


Theorem 2al2imi

Description: Removes two universal quantifiers from a statement. (Contributed by Andrew Salmon, 24-May-2011)

Ref Expression
Hypothesis 2al2imi.1 φ ψ χ
Assertion 2al2imi x y φ x y ψ x y χ

Proof

Step Hyp Ref Expression
1 2al2imi.1 φ ψ χ
2 1 al2imi y φ y ψ y χ
3 2 al2imi x y φ x y ψ x y χ