Theorem 19.21bbi 743

Description: Inference removing double quantifier.

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 742	. 2 ⊢ (φ → ∀yψ)
3	2	19.21bi 742	1 ⊢ (φ → ψ)

Syntax hints:   → wi 2  ∀wal 672

This theorem is referenced by:  trel 2048  pocl 2132  funun 2700

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-mp 6  ax-4 673

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