Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
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 11890 | . 2 ⊢ 2 = (1 + 1) | |
2 | 1 | eqcomi 2746 | 1 ⊢ (1 + 1) = 2 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1543 (class class class)co 7210 1c1 10727 + caddc 10729 2c2 11882 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 ax-7 2016 ax-9 2120 ax-ext 2708 |
This theorem depends on definitions: df-bi 210 df-an 400 df-ex 1788 df-cleq 2729 df-2 11890 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |