Theorem looinv 174

Description: The Inversion Axiom of the infinite-valued sentential logic (L-infinity) of Lukasiewicz. Using dfor2 400, we can see that this essentially expresses "disjunction commutes." Theorem *2.69 of [WhiteheadRussell] p. 108. (Contributed by NM, 12-Aug-2004.)

Assertion

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

Proof of Theorem looinv

Step	Hyp	Ref	Expression
1		imim1 70	. 2 |- (((ph -> ps) -> ps) -> ((ps -> ph) -> ((ph -> ps) -> ph)))
2		peirce 172	. 2 |- (((ph -> ps) -> ph) -> ph)
3	1, 2	syl6 29	1 |- (((ph -> ps) -> ps) -> ((ps -> ph) -> ph))

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by:  merco2  1501