Theorem 1e0p1 9750

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 9351	. 2 ⊢ (0 + 1) = 1
2	1	eqcomi 2236	1 ⊢ 1 = (0 + 1)

Syntax hints:   = wceq 1398  (class class class)co 6050  0cc0 8127  1c1 8128   + caddc 8130

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 1496  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-4 1559  ax-17 1575  ax-ial 1583  ax-ext 2214  ax-1cn 8220  ax-icn 8222  ax-addcl 8223  ax-mulcl 8225  ax-addcom 8227  ax-i2m1 8232  ax-0id 8235

This theorem depends on definitions:  df-bi 117  df-cleq 2225  df-clel 2228

This theorem is referenced by:  6p5e11  9781  7p4e11  9784  8p3e11  9789  9p2e11  9795  fz1ssfz0  10451  fz0to3un2pr  10457  fzo01  10561  bcp1nk  11124  pfx1  11395  arisum2  12185  ege2le3  12357  ef4p  12380  efgt1p2  12381  efgt1p  12382  bitsmod  12642  prmdiv  12932  ennnfonelem1  13158  mulgnn0p1  13850  dveflem  15591  lgsdir2lem3  15903  lgseisenlem1  15943