Theorem 1e0p1 9492

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 9098	. 2 ⊢ (0 + 1) = 1
2	1	eqcomi 2197	1 ⊢ 1 = (0 + 1)

Syntax hints:   = wceq 1364  (class class class)co 5919  0cc0 7874  1c1 7875   + caddc 7877

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 7967  ax-icn 7969  ax-addcl 7970  ax-mulcl 7972  ax-addcom 7974  ax-i2m1 7979  ax-0id 7982

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

This theorem is referenced by:  6p5e11  9523  7p4e11  9526  8p3e11  9531  9p2e11  9537  fz1ssfz0  10186  fz0to3un2pr  10192  fzo01  10286  bcp1nk  10836  arisum2  11645  ege2le3  11817  ef4p  11840  efgt1p2  11841  efgt1p  11842  prmdiv  12376  ennnfonelem1  12567  mulgnn0p1  13206  dveflem  14905  lgsdir2lem3  15187  lgseisenlem1  15227