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Theorem spnfw 1670
Description: Weak version of sp 1747. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 1-Aug-2017.) (Proof shortened by Wolf Lammen, 13-Aug-2017.)
Hypothesis
Ref Expression
spnfw.1 φx ¬ φ)
Assertion
Ref Expression
spnfw (xφφ)

Proof of Theorem spnfw
Dummy variable y is distinct from all other variables.
StepHypRef Expression
1 spnfw.1 . 2 φx ¬ φ)
2 idd 21 . 2 (x = y → (φφ))
31, 2spimw 1668 1 (xφφ)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  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-9 1654
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542
This theorem is referenced by:  spfalw  1672  19.8wOLD  1693
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