Theorem isolatiN 34503

Description: Properties that determine an ortholattice. (Contributed by NM, 18-Sep-2011.) (New usage is discouraged.)

Hypotheses

Ref	Expression
isolati.1	|- K e. Lat
isolati.2	|- K e. OP

Assertion

Ref	Expression
isolatiN	|- K e. OL

Proof of Theorem isolatiN

Step	Hyp	Ref	Expression
1		isolati.1	. 2 |- K e. Lat
2		isolati.2	. 2 |- K e. OP
3		isolat 34499	. 2 |- ( K e. OL <-> ( K e. Lat /\ K e. OP ) )
4	1, 2, 3	mpbir2an 955	1 |- K e. OL

Syntax hints:   e. wcel 1990   Latclat 17045   OPcops 34459   OLcol 34461

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-v 3202  df-in 3581  df-ol 34465

This theorem is referenced by: (None)