Theorem 1e0p1 9489

Description: The successor of zero. (Contributed by Mario Carneiro, 18-Feb-2014.)

Assertion

Ref	Expression
1e0p1	|- 1 = ( 0 + 1 )

Proof of Theorem 1e0p1

Step	Hyp	Ref	Expression
1		0p1e1 9096	. 2 |- ( 0 + 1 ) = 1
2	1	eqcomi 2197	1 |- 1 = ( 0 + 1 )

Syntax hints:   = wceq 1364  (class class class)co 5918   0cc0 7872   1c1 7873   + caddc 7875

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 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-17 1537  ax-ial 1545  ax-ext 2175  ax-1cn 7965  ax-icn 7967  ax-addcl 7968  ax-mulcl 7970  ax-addcom 7972  ax-i2m1 7977  ax-0id 7980

This theorem depends on definitions:  df-bi 117  df-cleq 2186  df-clel 2189

This theorem is referenced by:  6p5e11  9520  7p4e11  9523  8p3e11  9528  9p2e11  9534  fz1ssfz0  10183  fz0to3un2pr  10189  fzo01  10283  bcp1nk  10833  arisum2  11642  ege2le3  11814  ef4p  11837  efgt1p2  11838  efgt1p  11839  prmdiv  12373  ennnfonelem1  12564  mulgnn0p1  13203  dveflem  14872  lgsdir2lem3  15146  lgseisenlem1  15186