Theorem qlaxr2i 28492

Description: One of the conditions showing CH is an ortholattice. (This corresponds to axiom "ax-r2" in the Quantum Logic Explorer.) (Contributed by NM, 4-Aug-2004.) (New usage is discouraged.)

Hypotheses

Ref	Expression
qlaxr2.1	|- A e. CH
qlaxr2.2	|- B e. CH
qlaxr2.3	|- C e. CH
qlaxr2.4	|- A = B
qlaxr2.5	|- B = C

Assertion

Ref	Expression
qlaxr2i	|- A = C

Proof of Theorem qlaxr2i

Step	Hyp	Ref	Expression
1		qlaxr2.4	. 2 |- A = B
2		qlaxr2.5	. 2 |- B = C
3	1, 2	eqtri 2644	1 |- A = C

Syntax hints:   = wceq 1483   e. wcel 1990   CHcch 27786

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-ext 2602

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-cleq 2615

This theorem is referenced by: (None)