Theorem spi 1753

Description: Inference rule reversing generalization. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
spi.1	⊢ ∀xφ

Assertion

Ref	Expression
spi	⊢ φ

Proof of Theorem spi

Step	Hyp	Ref	Expression
1		spi.1	. 2 ⊢ ∀xφ
2		sp 1747	. 2 ⊢ (∀xφ → φ)
3	1, 2	ax-mp 5	1 ⊢ φ

Syntax hints:  ∀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:  darii  2303  barbari  2305  cesare  2307  camestres  2308  festino  2309  baroco  2310  cesaro  2311  camestros  2312  datisi  2313  disamis  2314  felapton  2317  darapti  2318  calemes  2319  dimatis  2320  fresison  2321  calemos  2322  fesapo  2323  bamalip  2324