Theorem 19.21bbi 1612

Description: Inference removing double quantifier. (Contributed by NM, 20-Apr-1994.)

Hypothesis

Ref	Expression
19.21bbi.1	⊢ (𝜑 → ∀𝑥∀𝑦𝜓)

Assertion

Ref	Expression
19.21bbi	⊢ (𝜑 → 𝜓)

Proof of Theorem 19.21bbi

Step	Hyp	Ref	Expression
1		19.21bbi.1	. . 3 ⊢ (𝜑 → ∀𝑥∀𝑦𝜓)
2	1	19.21bi 1611	. 2 ⊢ (𝜑 → ∀𝑦𝜓)
3	2	19.21bi 1611	1 ⊢ (𝜑 → 𝜓)

This proof depends on syntax axioms:   → wi 4  ∀wal 1400

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-4 1563

This theorem is used by:  pocl  4448  funun  5422  fununi  5449  imain  5463