Theorem loolin 173

Description: The Linearity Axiom of the infinite-valued sentential logic (L-infinity) of Lukasiewicz. For a version not using ax-3 8, see loolinALT 95. (Contributed by O'Cat, 12-Aug-2004.) (Proof shortened by Wolf Lammen, 2-Nov-2012.)

Assertion

Ref	Expression
loolin	|- (((ph -> ps) -> (ps -> ph)) -> (ps -> ph))

Proof of Theorem loolin

Step	Hyp	Ref	Expression
1		pm2.521 146	. 2 |- (-. (ph -> ps) -> (ps -> ph))
2		id 19	. 2 |- ((ps -> ph) -> (ps -> ph))
3	1, 2	ja 153	1 |- (((ph -> ps) -> (ps -> ph)) -> (ps -> ph))

This proof depends on syntax axioms:   -> wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is used by: (None)