Theorem spimvw 1927

Description: Specialization. Lemma 8 of [KalishMontague] p. 87. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 9-Apr-2017.)

Hypothesis

Ref	Expression
spimvw.1	|- ( x = y -> ( ph -> ps ) )

Assertion

Ref	Expression
spimvw	|- ( A. x ph -> ps )

Distinct variable groups:   x, y   ps, x

Allowed substitution hints:   ph( x, y)   ps( y)

Proof of Theorem spimvw

Step	Hyp	Ref	Expression
1		ax-5 1839	. 2 |- ( -. ps -> A. x -. ps )
2		spimvw.1	. 2 |- ( x = y -> ( ph -> ps ) )
3	1, 2	spimw 1926	1 |- ( A. x ph -> ps )

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-5 1839  ax-6 1888

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

This theorem is referenced by:  cbvalivw  1934  alcomiw  1971  fvn0ssdmfun  6350  bj-ax9-2  32891