Theorem 19.20i2 990

Description: Inference doubly quantifying both antecedent and consequent.

Hypothesis

Ref	Expression
19.20i.1	⊢ (φ → ψ)

Assertion

Ref	Expression
19.20i2	⊢ (∀x∀yφ → ∀x∀yψ)

Proof of Theorem 19.20i2

Step	Hyp	Ref	Expression
1		19.20i.1	. . 3 ⊢ (φ → ψ)
2	1	19.20i 989	. 2 ⊢ (∀yφ → ∀yψ)
3	2	19.20i 989	1 ⊢ (∀x∀yφ → ∀x∀yψ)

Syntax hints:   → wi 3  ∀wal 951

This theorem is referenced by:  dvelimdf 1246  mo 1386  2mo 1440  2eu6 1447  hbabd 1461  tz7.48lem 3940  fnoprabg 3997  axacndlem4 4934

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-mp 7  ax-gen 960  ax-4 970  ax-5o 972

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