Metamath Proof Explorer

Theorem 8p3e11

Description: 8 + 3 = 11. (Contributed by Mario Carneiro, 19-Apr-2015) (Revised by AV, 6-Sep-2021)

Ref Expression
Assertion 8p3e11 
|- ( 8 + 3 ) = ; 1 1

Proof

Step Hyp Ref Expression
1 8nn0 
 |-  8 e. NN0
2 2nn0 
 |-  2 e. NN0
3 0nn0 
 |-  0 e. NN0
4 df-3 
 |-  3 = ( 2 + 1 )
5 1e0p1 
 |-  1 = ( 0 + 1 )
6 8p2e10 
 |-  ( 8 + 2 ) = ; 1 0
7 1 2 3 4 5 6 6p5lem 
 |-  ( 8 + 3 ) = ; 1 1