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Theorem spfw 1830
 Description: Weak version of sp 1883. Uses only Tarski's FOL axiom schemes. Lemma 9 of [KalishMontague] p. 87. This may be the best we can do with minimal distinct variable conditions. (Contributed by NM, 19-Apr-2017.)
Hypotheses
Ref Expression
spfw.1
spfw.2
spfw.3
spfw.4
Assertion
Ref Expression
spfw
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem spfw
StepHypRef Expression
1 spfw.2 . . 3
2 alim 1653 . . 3
3 spfw.3 . . . 4
4 spfw.4 . . . . . 6
54biimprd 223 . . . . 5
65equcoms 1819 . . . 4
73, 6spimw 1807 . . 3
81, 2, 7syl56 32 . 2
9 spfw.1 . . 3
104biimpd 207 . . 3
119, 10spimw 1807 . 2
128, 11mpg 1641 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 184  wal 1403 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814 This theorem depends on definitions:  df-bi 185  df-ex 1634 This theorem is referenced by:  spw  1831
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