Theorem spsd 2229

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 2225	. 2 ⊢ (∀𝑥𝜓 → 𝜓)
2		spsd.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
3	1, 2	syl5 35	1 ⊢ (𝜑 → (∀𝑥𝜓 → 𝜒))

Syntax hints:   → wi 4  ∀wal 1565

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-12 2219

This theorem depends on definitions:  df-bi 210  df-ex 1807

This theorem is referenced by:  axc11v  2306  axc11rv  2307  equs5av  2318  equvel  2494  nfsb4t  2537  dfmoeu  2569  moexexlem  2660  2eu6  2690  zorn2lem4  10482  zorn2lem5  10483  axpowndlem3  10583  axacndlem5  10595  mh-setindnd  36936  axc11n11r  37196  wl-equsal1i  38086  axc5c4c711  45002