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Theorem spim 1717
 Description: Specialization, using implicit substitution. Compare Lemma 14 of [Tarski] p. 70. The spim 1717 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 rewritten by Jim Kingdon, 10-Jun-2018.)
Hypotheses
Ref Expression
spim.1
spim.2
Assertion
Ref Expression
spim

Proof of Theorem spim
StepHypRef Expression
1 spim.1 . . 3
21nfri 1500 . 2
3 spim.2 . 2
42, 3spimh 1716 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1330  wnf 1437 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-4 1488  ax-i9 1511  ax-ial 1515 This theorem depends on definitions:  df-bi 116  df-nf 1438 This theorem is referenced by:  cbv3  1721  chvar  1731  spimv  1784  2spim  13137
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