Theorem 19.21bbi 2183

Description: Inference removing two universal quantifiers. Version of 19.21bi 2182 with two quantifiers. (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 2182	. 2 ⊢ (𝜑 → ∀𝑦𝜓)
3	2	19.21bi 2182	1 ⊢ (𝜑 → 𝜓)

Syntax hints:   → wi 4  ∀wal 1539

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-12 2171

This theorem depends on definitions:  df-bi 206  df-ex 1782

This theorem is referenced by:  2mo  2643  poclOLD  5589  funun  6583  fununi  6612  trclfvcotr  14938  acycgrcycl  33967  pm14.24  42960