Theorem 1e0p1 9797

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 9397	. 2 ⊢ (0 + 1) = 1
2	1	eqcomi 2242	1 ⊢ 1 = (0 + 1)

Syntax hints:   = wceq 1402  (class class class)co 6075  0cc0 8169  1c1 8170   + caddc 8172

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 1500  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-4 1563  ax-17 1579  ax-ial 1587  ax-ext 2220  ax-1cn 8262  ax-icn 8264  ax-addcl 8265  ax-mulcl 8267  ax-addcom 8269  ax-i2m1 8274  ax-0id 8277

This theorem depends on definitions:  df-bi 117  df-cleq 2231  df-clel 2234

This theorem is referenced by:  6p5e11  9828  7p4e11  9831  8p3e11  9836  9p2e11  9842  fz1ssfz0  10502  fz0to3un2pr  10508  fzo01  10612  bcp1nk  11178  pfx1  11453  arisum2  12244  ege2le3  12416  ef4p  12439  efgt1p2  12440  efgt1p  12441  bitsmod  12701  prmdiv  12991  ballotfilemii  13224  ballotfilem1c  13229  ennnfonelem1  13276  mulgnn0p1  13913  dveflem  15750  lgsdir2lem3  16063  lgseisenlem1  16103