Theorem 1e0p1 9498

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 9104	. 2 ⊢ (0 + 1) = 1
2	1	eqcomi 2200	1 ⊢ 1 = (0 + 1)

Syntax hints:   = wceq 1364  (class class class)co 5922  0cc0 7879  1c1 7880   + caddc 7882

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 1461  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-4 1524  ax-17 1540  ax-ial 1548  ax-ext 2178  ax-1cn 7972  ax-icn 7974  ax-addcl 7975  ax-mulcl 7977  ax-addcom 7979  ax-i2m1 7984  ax-0id 7987

This theorem depends on definitions:  df-bi 117  df-cleq 2189  df-clel 2192

This theorem is referenced by:  6p5e11  9529  7p4e11  9532  8p3e11  9537  9p2e11  9543  fz1ssfz0  10192  fz0to3un2pr  10198  fzo01  10292  bcp1nk  10854  arisum2  11664  ege2le3  11836  ef4p  11859  efgt1p2  11860  efgt1p  11861  prmdiv  12403  ennnfonelem1  12624  mulgnn0p1  13263  dveflem  14962  lgsdir2lem3  15271  lgseisenlem1  15311