Theorem spimev 1833

Description: Distinct-variable version of spime 1719. (Contributed by NM, 5-Aug-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 1508	. 2 |- F/ x ph
2		spimev.1	. 2 |- ( x = y -> ( ph -> ps ) )
3	1, 2	spime 1719	1 |- ( ph -> E. x ps )

Syntax hints:   -> wi 4   E.wex 1468

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437

This theorem is referenced by:  speiv  1834  rnxpid  4968