Metamath Proof Explorer


Theorem rblem2

Description: Used to rederive the Lukasiewicz axioms from Russell-Bernays'. (Contributed by Anthony Hart, 18-Aug-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion rblem2
|- ( -. ( ch \/ ph ) \/ ( ch \/ ( ph \/ ps ) ) )

Proof

Step Hyp Ref Expression
1 rb-ax2
 |-  ( -. ( ps \/ ph ) \/ ( ph \/ ps ) )
2 rb-ax3
 |-  ( -. ph \/ ( ps \/ ph ) )
3 1 2 rbsyl
 |-  ( -. ph \/ ( ph \/ ps ) )
4 rb-ax1
 |-  ( -. ( -. ph \/ ( ph \/ ps ) ) \/ ( -. ( ch \/ ph ) \/ ( ch \/ ( ph \/ ps ) ) ) )
5 3 4 anmp
 |-  ( -. ( ch \/ ph ) \/ ( ch \/ ( ph \/ ps ) ) )