Metamath Proof Explorer


Theorem pjoml5i

Description: The orthomodular law. Remark in Kalmbach p. 22. (Contributed by NM, 12-Jun-2006) (New usage is discouraged.)

Ref Expression
Hypotheses pjoml2.1 A C
pjoml2.2 B C
Assertion pjoml5i A A A B = A B

Proof

Step Hyp Ref Expression
1 pjoml2.1 A C
2 pjoml2.2 B C
3 1 2 chub1i A A B
4 1 2 chjcli A B C
5 1 4 pjoml2i A A B A A A B = A B
6 3 5 ax-mp A A A B = A B