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Theorem spfw 1691
 Description: Weak version of sp 1747. 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. TO DO: Do we need this theorem? If not, maybe it should be deleted. (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 ax-5 1557 . . 3
3 spfw.3 . . . 4
4 spfw.4 . . . . . 6
54biimprd 214 . . . . 5
65equcoms 1681 . . . 4
73, 6spimw 1668 . . 3
81, 2, 7syl56 30 . 2
9 spfw.1 . . 3
104biimpd 198 . . 3
119, 10spimw 1668 . 2
128, 11mpg 1548 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 176  wal 1540 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542 This theorem is referenced by:  spnfwOLD  1692
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