Theorem spimv 1692

Description: A version of spim 1626 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 1421	. 2 |- F/ x ps
2		spimv.1	. 2 |- ( x = y -> ( ph -> ps ) )
3	1, 2	spim 1626	1 |- ( A. x ph -> ps )

Syntax hints:   -> wi 4   A.wal 1241

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427

This theorem depends on definitions:  df-bi 110  df-nf 1350

This theorem is referenced by:  aev  1693  ax16i  1738  spv  1740  reu6  2730  el  3931