Theorem spimev 1741

Description: Distinct-variable version of spime 1629. (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 1421	. 2 |- F/ x ph
2		spimev.1	. 2 |- ( x = y -> ( ph -> ps ) )
3	1, 2	spime 1629	1 |- ( ph -> E. x ps )

Syntax hints:   -> wi 4   E.wex 1381

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-tru 1246  df-nf 1350

This theorem is referenced by:  speiv  1742  rnxpid  4755