Theorem spsd 1755

Description: Deduction generalizing antecedent. (Contributed by NM, 17-Aug-1994.)

Hypothesis

Ref	Expression
spsd.1	⊢ (φ → (ψ → χ))

Assertion

Ref	Expression
spsd	⊢ (φ → (∀xψ → χ))

Proof of Theorem spsd

Step	Hyp	Ref	Expression
1		sp 1747	. 2 ⊢ (∀xψ → ψ)
2		spsd.1	. 2 ⊢ (φ → (ψ → χ))
3	1, 2	syl5 28	1 ⊢ (φ → (∀xψ → χ))

Syntax hints:   → wi 4  ∀wal 1540

This theorem was proved from 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 theorem depends on definitions:  df-bi 177  df-ex 1542

This theorem is referenced by:  ax10lem4  1941  moexex  2273