Theorem spimev 1884

Description: Distinct-variable version of spime 1764. (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 1551	. 2 |- F/ x ph
2		spimev.1	. 2 |- ( x = y -> ( ph -> ps ) )
3	1, 2	spime 1764	1 |- ( ph -> E. x ps )

Syntax hints:   -> wi 4   E.wex 1515

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1470  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1484

This theorem is referenced by:  speiv  1885  cbvexvw  1944  rnxpid  5117