Theorem 1p1e2apr1 30828

Description: One plus one equals two. Using proof-shortening techniques pioneered by Mr. Mel L. O'Cat, along with the latest supercomputer technology, Prof. Loof Lirpa and colleagues were able to shorten Whitehead and Russell's 360-page proof that 1+1=2 in Principia Mathematica to this remarkable proof only two steps long, thus establishing a new world's record for this famous theorem. (Contributed by Prof. Loof Lirpa, 1-Apr-2008.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
1p1e2apr1	⊢ (1 + 1) = 2

Proof of Theorem 1p1e2apr1

Step	Hyp	Ref	Expression
1		df-2 12309	. 2 ⊢ 2 = (1 + 1)
2	1	eqcomi 2771	1 ⊢ (1 + 1) = 2

This proof depends on syntax axioms:   = wceq 1569  (class class class)co 7412  1c1 11107   + caddc 11109  2c2 12301

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037  ax-9 2152  ax-ext 2734

This proof depends on definitions:  df-bi 210  df-an 401  df-ex 1809  df-cleq 2754  df-2 12309

This theorem is used by: (None)