Theorem 1e0p1 9630

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 9235	. 2 ⊢ (0 + 1) = 1
2	1	eqcomi 2233	1 ⊢ 1 = (0 + 1)

Syntax hints:   = wceq 1395  (class class class)co 6007  0cc0 8010  1c1 8011   + caddc 8013

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 1493  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-4 1556  ax-17 1572  ax-ial 1580  ax-ext 2211  ax-1cn 8103  ax-icn 8105  ax-addcl 8106  ax-mulcl 8108  ax-addcom 8110  ax-i2m1 8115  ax-0id 8118

This theorem depends on definitions:  df-bi 117  df-cleq 2222  df-clel 2225

This theorem is referenced by:  6p5e11  9661  7p4e11  9664  8p3e11  9669  9p2e11  9675  fz1ssfz0  10325  fz0to3un2pr  10331  fzo01  10434  bcp1nk  10996  pfx1  11251  arisum2  12026  ege2le3  12198  ef4p  12221  efgt1p2  12222  efgt1p  12223  bitsmod  12483  prmdiv  12773  ennnfonelem1  12994  mulgnn0p1  13686  dveflem  15416  lgsdir2lem3  15725  lgseisenlem1  15765