Theorem rb-ax1

Description: The first of four axioms in the Russell-Bernays axiom system. (Contributed by Anthony Hart, 13-Aug-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	rb-ax1	|- ( -. ( -. ps \/ ch ) \/ ( -. ( ph \/ ps ) \/ ( ph \/ ch ) ) )

Proof

Step	Hyp	Ref	Expression
1		orim2	|- ( ( ps -> ch ) -> ( ( ph \/ ps ) -> ( ph \/ ch ) ) )
2		imor	|- ( ( ps -> ch ) <-> ( -. ps \/ ch ) )
3		imor	|- ( ( ( ph \/ ps ) -> ( ph \/ ch ) ) <-> ( -. ( ph \/ ps ) \/ ( ph \/ ch ) ) )
4	1 2 3	3imtr3i	|- ( ( -. ps \/ ch ) -> ( -. ( ph \/ ps ) \/ ( ph \/ ch ) ) )
5	4	imori	|- ( -. ( -. ps \/ ch ) \/ ( -. ( ph \/ ps ) \/ ( ph \/ ch ) ) )