Theorem spimev 2259

Description: Distinct-variable version of spime 2256. (Contributed by NM, 10-Jan-1993.)

Hypothesis

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

Assertion

Ref	Expression
spimev	|- ( ph -> E. x ps )

Distinct variable group:   ph, x

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

Proof of Theorem spimev

Step	Hyp	Ref	Expression
1		nfv 1843	. 2 |- F/ x ph
2		spimev.1	. 2 |- ( x = y -> ( ph -> ps ) )
3	1, 2	spime 2256	1 |- ( ph -> E. x ps )

Syntax hints:   -> wi 4   E.wex 1704

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  ax-7 1935  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710

This theorem is referenced by:  axsep  4780  dtru  4857  zfpair  4904  fvn0ssdmfun  6350  refimssco  37913  rlimdmafv  41257  elsprel  41725