Theorem spimev 1999

Description: Distinct-variable version of spime 1976. (Contributed by NM, 5-Aug-1993.)

Hypothesis

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

Assertion

Ref	Expression
spimev	|- (ph -> E.xps)

Distinct variable group:   ph,x

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

Proof of Theorem spimev

Step	Hyp	Ref	Expression
1		nfv 1619	. 2 |- F/xph
2		spimev.1	. 2 |- (x = y -> (ph -> ps))
3	1, 2	spime 1976	1 |- (ph -> E.xps)

Syntax hints:   -> wi 4  E.wex 1541

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545

This theorem is referenced by:  speiv  2000