Theorem spim 2006

Description: Specialization, using implicit substitution. Compare Lemma 14 of [Tarski] p. 70. The spim 2006 series of theorems requires that only one direction of the substitution hypothesis hold. (Contributed by NM, 10-Jan-1993.) (Revised by Mario Carneiro, 3-Oct-2016.) (Proof shortened by Wolf Lammen, 18-Feb-2018.)

Hypotheses

Ref	Expression
spim.1
spim.2

Assertion

Ref	Expression
spim

Proof of Theorem spim

Step	Hyp	Ref	Expression
1		spim.1	. 2
2		ax6e 2002	. . 3
3		spim.2	. . 3
4	2, 3	eximii 1658	. 2
5	1, 4	19.36i 1965	1

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

This theorem is referenced by:  spimv  2009  chvar  2013  cbv3  2015

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-10 1837  ax-12 1854  ax-13 1999

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