Theorem dalem-ccly

Description: Lemma for dath . Frequently-used utility lemma. (Contributed by NM, 15-Aug-2012)

	Ref	Expression
Hypothesis	da.ps0	|- ( ps <-> ( ( c e. A /\ d e. A ) /\ -. c .<_ Y /\ ( d =/= c /\ -. d .<_ Y /\ C .<_ ( c .\/ d ) ) ) )
Assertion	dalem-ccly	|- ( ps -> -. c .<_ Y )

Proof

Step	Hyp	Ref	Expression
1		da.ps0	|- ( ps <-> ( ( c e. A /\ d e. A ) /\ -. c .<_ Y /\ ( d =/= c /\ -. d .<_ Y /\ C .<_ ( c .\/ d ) ) ) )
2	1	simp2bi	|- ( ps -> -. c .<_ Y )