Theorem 19.21bbi 2230

Description: Inference removing two universal quantifiers. Version of 19.21bi 2229 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 2229	. 2 ⊢ (𝜑 → ∀𝑦𝜓)
3	2	19.21bi 2229	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 1945  ax-6 2002  ax-7 2043  ax-12 2216

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

This theorem is used by:  2mo  2676  funun  6614  fununi  6645  trclfvcotr  15205  acycgrcycl  30810  onvfowev  36091  pm14.24  45676