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Theorem spim 1957
 Description: Specialization, using implicit substitution. Compare Lemma 14 of [Tarski] p. 70. The spim 1957 series of theorems requires that only one direction of the substitution hypothesis hold. (Contributed by NM, 5-Aug-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 a9e 1952 . . 3
3 spim.2 . . 3
42, 3eximii 1587 . 2
51, 419.36i 1893 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1549  wnf 1553 This theorem is referenced by:  spimeOLD  1959  spimv  1963  chvar  1968  cbv3  1971 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-11 1761  ax-12 1950 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554
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