Theorem 1p1e2apr1 30832

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 12313	. 2 ⊢ 2 = (1 + 1)
2	1	eqcomi 2775	1 ⊢ (1 + 1) = 2

This proof depends on syntax axioms:   = wceq 1570  (class class class)co 7416  1c1 11111   + caddc 11113  2c2 12305

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-9 2156  ax-ext 2738

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1813  df-cleq 2758  df-2 12313

This theorem is used by: (None)