Theorem 1e0p1 9651

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 9256	. 2 ⊢ (0 + 1) = 1
2	1	eqcomi 2235	1 ⊢ 1 = (0 + 1)

Syntax hints:   = wceq 1397  (class class class)co 6017  0cc0 8031  1c1 8032   + caddc 8034

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 1495  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-4 1558  ax-17 1574  ax-ial 1582  ax-ext 2213  ax-1cn 8124  ax-icn 8126  ax-addcl 8127  ax-mulcl 8129  ax-addcom 8131  ax-i2m1 8136  ax-0id 8139

This theorem depends on definitions:  df-bi 117  df-cleq 2224  df-clel 2227

This theorem is referenced by:  6p5e11  9682  7p4e11  9685  8p3e11  9690  9p2e11  9696  fz1ssfz0  10351  fz0to3un2pr  10357  fzo01  10460  bcp1nk  11023  pfx1  11283  arisum2  12059  ege2le3  12231  ef4p  12254  efgt1p2  12255  efgt1p  12256  bitsmod  12516  prmdiv  12806  ennnfonelem1  13027  mulgnn0p1  13719  dveflem  15449  lgsdir2lem3  15758  lgseisenlem1  15798