Theorem spnfw 1928

Description: Weak version of sp 2053. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 1-Aug-2017.) (Proof shortened by Wolf Lammen, 13-Aug-2017.)

Hypothesis

Ref	Expression
spnfw.1	|- ( -. ph -> A. x -. ph )

Assertion

Ref	Expression
spnfw	|- ( A. x ph -> ph )

Proof of Theorem spnfw

Dummy variable y is distinct from all other variables.

Step	Hyp	Ref	Expression
1		spnfw.1	. 2 |- ( -. ph -> A. x -. ph )
2		idd 24	. 2 |- ( x = y -> ( ph -> ph ) )
3	1, 2	spimw 1926	1 |- ( A. x ph -> ph )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-6 1888

This theorem depends on definitions:  df-bi 197  df-ex 1705

This theorem is referenced by:  spfalw  1929