Theorem 1e0p1 9652

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 9257	. 2 ⊢ (0 + 1) = 1
2	1	eqcomi 2235	1 ⊢ 1 = (0 + 1)

Syntax hints:   = wceq 1397  (class class class)co 6018  0cc0 8032  1c1 8033   + caddc 8035

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 1495  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-4 1558  ax-17 1574  ax-ial 1582  ax-ext 2213  ax-1cn 8125  ax-icn 8127  ax-addcl 8128  ax-mulcl 8130  ax-addcom 8132  ax-i2m1 8137  ax-0id 8140

This theorem depends on definitions:  df-bi 117  df-cleq 2224  df-clel 2227

This theorem is referenced by:  6p5e11  9683  7p4e11  9686  8p3e11  9691  9p2e11  9697  fz1ssfz0  10352  fz0to3un2pr  10358  fzo01  10462  bcp1nk  11025  pfx1  11288  arisum2  12078  ege2le3  12250  ef4p  12273  efgt1p2  12274  efgt1p  12275  bitsmod  12535  prmdiv  12825  ennnfonelem1  13046  mulgnn0p1  13738  dveflem  15469  lgsdir2lem3  15778  lgseisenlem1  15818