Theorem bnj562

Description: Technical lemma for bnj852 . This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypotheses	bnj562.18	|- ( si <-> ( m e. D /\ n = suc m /\ p e. m ) )
	bnj562.19	|- ( et <-> ( m e. D /\ n = suc m /\ p e. _om /\ m = suc p ) )
	bnj562.38	|- ( ( R _FrSe A /\ ta /\ si ) -> ph" )
Assertion	bnj562	|- ( ( R _FrSe A /\ ta /\ et ) -> ph" )

Proof

Step	Hyp	Ref	Expression
1		bnj562.18	|- ( si <-> ( m e. D /\ n = suc m /\ p e. m ) )
2		bnj562.19	|- ( et <-> ( m e. D /\ n = suc m /\ p e. _om /\ m = suc p ) )
3		bnj562.38	|- ( ( R _FrSe A /\ ta /\ si ) -> ph" )
4	1 2	bnj556	|- ( et -> si )
5	4 3	syl3an3	|- ( ( R _FrSe A /\ ta /\ et ) -> ph" )