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Theorem spfalwOLD 1699
 Description: Obsolete proof of spfalw 1672 as of 25-Dec-2017. (Contributed by NM, 23-Apr-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
spfalwOLD.1 ¬ φ
Assertion
Ref Expression
spfalwOLD (xφφ)

Proof of Theorem spfalwOLD
Dummy variable y is distinct from all other variables.
StepHypRef Expression
1 spfalwOLD.1 . . . 4 ¬ φ
21bifal 1327 . . 3 (φ ↔ ⊥ )
32a1i 10 . 2 (x = y → (φ ↔ ⊥ ))
43spw 1694 1 (xφφ)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 176   ⊥ wfal 1317  ∀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-tru 1319  df-fal 1320  df-ex 1542 This theorem is referenced by: (None)
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