Theorem 19.21bbi 2191

Description: Inference removing two universal quantifiers. Version of 19.21bi 2190 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 2190	. 2 ⊢ (𝜑 → ∀𝑦𝜓)
3	2	19.21bi 2190	1 ⊢ (𝜑 → 𝜓)

Syntax hints:   → wi 4  ∀wal 1535

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-12 2178

This theorem depends on definitions:  df-bi 207  df-ex 1778

This theorem is referenced by:  2mo  2651  poclOLD  5616  funun  6624  fununi  6653  trclfvcotr  15058  acycgrcycl  35115  pm14.24  44401