Theorem 19.21bbi 1865

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 1758	. 2 ⊢ (φ → ∀yψ)
3	2	19.21bi 1758	1 ⊢ (φ → ψ)

This proof depends on syntax axioms:   → wi 4  ∀wal 1540

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746

This proof depends on definitions:  df-bi 177  df-ex 1542

This theorem is used by:  ssfin  4471  funun  5147  fnfrec  6321