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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
StepHypRef Expression
1 spim.1 . 2
2 ax6e 2002 . . 3
3 spim.2 . . 3
42, 3eximii 1658 . 2
51, 419.36i 1965 1
 Colors of variables: wff setvar class 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
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