Theorem spimed 2007

Description: Deduction version of spime 2008. (Contributed by NM, 14-May-1993.) (Revised by Mario Carneiro, 3-Oct-2016.) (Proof shortened by Wolf Lammen, 19-Feb-2018.)

Hypotheses

Ref	Expression
spimed.1
spimed.2

Assertion

Ref	Expression
spimed

Proof of Theorem spimed

Step	Hyp	Ref	Expression
1		spimed.1	. . 3
2	1	nfrd 1875	. 2
3		ax6e 2002	. . . 4
4		spimed.2	. . . 4
5	3, 4	eximii 1658	. . 3
6	5	19.35i 1689	. 2
7	2, 6	syl6 33	1

Syntax hints:  ->wi 4  A.wal 1393  E.wex 1612  F/wnf 1616

This theorem is referenced by:  spime  2008  2ax6elem  2193

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-12 1854  ax-13 1999

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617