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Theorem spim 1928
 Description: Specialization, using implicit substitution. Compare Lemma 14 of [Tarski] p. 70. The spim 1928 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.)
Hypotheses
Ref Expression
spim.1
spim.2
Assertion
Ref Expression
spim

Proof of Theorem spim
StepHypRef Expression
1 spim.1 . 2
2 spim.2 . . 3
32ax-gen 1536 . 2
4 spimt 1927 . 2
51, 3, 4mp2an 653 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1530  wnf 1534 This theorem is referenced by:  spime  1929  chvar  1939  spimv  1943 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535
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