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

Theorem 1p2e3 8520
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 8464 . 2  |-  2  e.  CC
2 ax-1cn 7417 . 2  |-  1  e.  CC
3 2p1e3 8519 . 2  |-  ( 2  +  1 )  =  3
41, 2, 3addcomli 7606 1  |-  ( 1  +  2 )  =  3
Colors of variables: wff set class
Syntax hints:    = wceq 1289  (class class class)co 5634   1c1 7330    + caddc 7332   2c2 8444   3c3 8445
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-11 1442  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-resscn 7416  ax-1cn 7417  ax-1re 7418  ax-addrcl 7421  ax-addcom 7424
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-in 3003  df-ss 3010  df-2 8452  df-3 8453
This theorem is referenced by:  binom3  10036  3lcm2e6woprm  11161  1kp2ke3k  11308
  Copyright terms: Public domain W3C validator