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	⊢ (∀xφ → φ)

Proof of Theorem spfalwOLD

Dummy variable y is distinct from all other variables.

Step	Hyp	Ref	Expression
1		spfalwOLD.1	. . . 4 ⊢ ¬ φ
2	1	bifal 1327	. . 3 ⊢ (φ ↔ ⊥ )
3	2	a1i 10	. 2 ⊢ (x = y → (φ ↔ ⊥ ))
4	3	spw 1694	1 ⊢ (∀xφ → φ)

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)