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Theorem spnfwOLD 1692
 Description: Weak version of sp 1747. Uses only Tarski's FOL axiom schemes. Obsolete version of spnfw 1670 as of 13-Aug-2017. (Contributed by NM, 1-Aug-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
spnfw.3 φx ¬ φ)
Assertion
Ref Expression
spnfwOLD (xφφ)

Proof of Theorem spnfwOLD
Dummy variable y is distinct from all other variables.
StepHypRef Expression
1 spnfw.3 . 2 φx ¬ φ)
2 ax-17 1616 . 2 (xφyxφ)
3 ax-17 1616 . 2 φy ¬ φ)
4 biidd 228 . 2 (x = y → (φφ))
51, 2, 3, 4spfw 1691 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-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: (None)
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