Theorem looinv 194

Description: The Inversion Axiom of the infinite-valued sentential logic (L-infinity) of Lukasiewicz. Using dfor2 427, we can see that this essentially expresses "disjunction commutes." Theorem *2.69 of [WhiteheadRussell] p. 108. It is a special instance of the axiom "Roll", see peirceroll 85. (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 83	. 2 |- ( ( ( ph -> ps ) -> ps ) -> ( ( ps -> ph ) -> ( ( ph -> ps ) -> ph ) ) )
2		peirce 193	. 2 |- ( ( ( ph -> ps ) -> ph ) -> ph )
3	1, 2	syl6 35	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  1661  bj-looinvi  32554