Theorem 1e0p1 9517

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 9123	. 2 ⊢ (0 + 1) = 1
2	1	eqcomi 2200	1 ⊢ 1 = (0 + 1)

Syntax hints:   = wceq 1364  (class class class)co 5925  0cc0 7898  1c1 7899   + caddc 7901

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 7991  ax-icn 7993  ax-addcl 7994  ax-mulcl 7996  ax-addcom 7998  ax-i2m1 8003  ax-0id 8006

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

This theorem is referenced by:  6p5e11  9548  7p4e11  9551  8p3e11  9556  9p2e11  9562  fz1ssfz0  10211  fz0to3un2pr  10217  fzo01  10311  bcp1nk  10873  arisum2  11683  ege2le3  11855  ef4p  11878  efgt1p2  11879  efgt1p  11880  bitsmod  12140  prmdiv  12430  ennnfonelem1  12651  mulgnn0p1  13341  dveflem  15070  lgsdir2lem3  15379  lgseisenlem1  15419