Theorem 19.21bbi 2229

Description: Inference removing two universal quantifiers. Version of 19.21bi 2228 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 2228	. 2 ⊢ (𝜑 → ∀𝑦𝜓)
3	2	19.21bi 2228	1 ⊢ (𝜑 → 𝜓)

This proof depends on syntax axioms:   → wi 4  ∀wal 1568

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-12 2216

This proof depends on definitions:  df-bi 210  df-ex 1813

This theorem is used by:  2mo  2678  funun  6586  fununi  6615  trclfvcotr  15070  onvfowev  35657  acycgrcycl  35676  pm14.24  45200