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Mirrors > Home > MPE Home > Th. List > 1p1e2apr1 | Structured version Visualization version GIF version |
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.) |
Ref | Expression |
---|---|
1p1e2apr1 | ⊢ (1 + 1) = 2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-2 11694 | . 2 ⊢ 2 = (1 + 1) | |
2 | 1 | eqcomi 2830 | 1 ⊢ (1 + 1) = 2 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1533 (class class class)co 7150 1c1 10532 + caddc 10534 2c2 11686 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 ax-9 2120 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-ex 1777 df-cleq 2814 df-2 11694 |
This theorem is referenced by: (None) |
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