Theorem spimv 1732

Description: A version of spim 1666 with a distinct variable requirement instead of a bound variable hypothesis. (Contributed by NM, 5-Aug-1993.)

Hypothesis

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

Assertion

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

Distinct variable group:   ps, x

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

Proof of Theorem spimv

Step	Hyp	Ref	Expression
1		nfv 1461	. 2 |- F/ x ps
2		spimv.1	. 2 |- ( x = y -> ( ph -> ps ) )
3	1, 2	spim 1666	1 |- ( A. x ph -> ps )

Syntax hints:   -> wi 4   A.wal 1282

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467

This theorem depends on definitions:  df-bi 115  df-nf 1390

This theorem is referenced by:  aev  1733  ax16i  1779  spv  1781  reu6  2781  el  3952