Theorem 1e0p1 9384

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 8992	. 2 ⊢ (0 + 1) = 1
2	1	eqcomi 2174	1 ⊢ 1 = (0 + 1)

Syntax hints:   = wceq 1348  (class class class)co 5853  0cc0 7774  1c1 7775   + caddc 7777

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 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-17 1519  ax-ial 1527  ax-ext 2152  ax-1cn 7867  ax-icn 7869  ax-addcl 7870  ax-mulcl 7872  ax-addcom 7874  ax-i2m1 7879  ax-0id 7882

This theorem depends on definitions:  df-bi 116  df-cleq 2163  df-clel 2166

This theorem is referenced by:  6p5e11  9415  7p4e11  9418  8p3e11  9423  9p2e11  9429  fz1ssfz0  10073  fz0to3un2pr  10079  fzo01  10172  bcp1nk  10696  arisum2  11462  ege2le3  11634  ef4p  11657  efgt1p2  11658  efgt1p  11659  prmdiv  12189  ennnfonelem1  12362  dveflem  13481  lgsdir2lem3  13725