Metamath Proof Explorer


Theorem atcvr1

Description: An atom is covered by its join with a different atom. (Contributed by NM, 7-Feb-2012)

Ref Expression
Hypotheses atcvr1.j ˙=joinK
atcvr1.c C=K
atcvr1.a A=AtomsK
Assertion atcvr1 KHLPAQAPQPCP˙Q

Proof

Step Hyp Ref Expression
1 atcvr1.j ˙=joinK
2 atcvr1.c C=K
3 atcvr1.a A=AtomsK
4 hlomcmcv KHLKOMLKCLatKCvLat
5 1 2 3 cvlatcvr1 KOMLKCLatKCvLatPAQAPQPCP˙Q
6 4 5 syl3an1 KHLPAQAPQPCP˙Q