Theorem 1e0p1 9359

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 8967	. 2 ⊢ (0 + 1) = 1
2	1	eqcomi 2169	1 ⊢ 1 = (0 + 1)

Syntax hints:   = wceq 1343  (class class class)co 5841  0cc0 7749  1c1 7750   + caddc 7752

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1435  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-4 1498  ax-17 1514  ax-ial 1522  ax-ext 2147  ax-1cn 7842  ax-icn 7844  ax-addcl 7845  ax-mulcl 7847  ax-addcom 7849  ax-i2m1 7854  ax-0id 7857

This theorem depends on definitions:  df-bi 116  df-cleq 2158  df-clel 2161

This theorem is referenced by:  6p5e11  9390  7p4e11  9393  8p3e11  9398  9p2e11  9404  fz1ssfz0  10048  fz0to3un2pr  10054  fzo01  10147  bcp1nk  10671  arisum2  11436  ege2le3  11608  ef4p  11631  efgt1p2  11632  efgt1p  11633  prmdiv  12163  ennnfonelem1  12336  dveflem  13287  lgsdir2lem3  13531