Theorem 19.21bbi 1451

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 1450	. 2 ⊢ (𝜑 → ∀𝑦𝜓)
3	2	19.21bi 1450	1 ⊢ (𝜑 → 𝜓)

Syntax hints:   → wi 4  ∀wal 1241

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-4 1400

This theorem is referenced by:  pocl  4040  funun  4944  fununi  4967  imain  4981