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Theorem spimw 1680
 Description: Specialization. Lemma 8 of [KalishMontague] p. 87. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 19-Apr-2017.) (Proof shortened by Wolf Lammen, 7-Aug-2017.)
Hypotheses
Ref Expression
spimw.1
spimw.2
Assertion
Ref Expression
spimw
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem spimw
StepHypRef Expression
1 ax9v 1667 . 2
2 spimw.1 . . 3
3 spimw.2 . . 3
42, 3spimfw 1656 . 2
51, 4ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1549 This theorem is referenced by:  spimvw  1681  spnfw  1682  cbvaliw  1685  spfw  1703 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-9 1666 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551
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