ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  1p2e3 Unicode version

Theorem 1p2e3 9051
Description: 1 + 2 = 3 (common case). (Contributed by David A. Wheeler, 8-Dec-2018.)
Assertion
Ref Expression
1p2e3  |-  ( 1  +  2 )  =  3

Proof of Theorem 1p2e3
StepHypRef Expression
1 2cn 8988 . 2  |-  2  e.  CC
2 ax-1cn 7903 . 2  |-  1  e.  CC
3 2p1e3 9050 . 2  |-  ( 2  +  1 )  =  3
41, 2, 3addcomli 8100 1  |-  ( 1  +  2 )  =  3
Colors of variables: wff set class
Syntax hints:    = wceq 1353  (class class class)co 5874   1c1 7811    + caddc 7813   2c2 8968   3c3 8969
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159  ax-resscn 7902  ax-1cn 7903  ax-1re 7904  ax-addrcl 7907  ax-addcom 7910
This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-in 3135  df-ss 3142  df-2 8976  df-3 8977
This theorem is referenced by:  binom3  10634  3lcm2e6woprm  12080  1kp2ke3k  14358
  Copyright terms: Public domain W3C validator