Theorem 1e0p1 9216

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 8827	. 2 |- ( 0 + 1 ) = 1
2	1	eqcomi 2141	1 |- 1 = ( 0 + 1 )

Syntax hints:   = wceq 1331  (class class class)co 5767   0cc0 7613   1c1 7614   + caddc 7616

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 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-17 1506  ax-ial 1514  ax-ext 2119  ax-1cn 7706  ax-icn 7708  ax-addcl 7709  ax-mulcl 7711  ax-addcom 7713  ax-i2m1 7718  ax-0id 7721

This theorem depends on definitions:  df-bi 116  df-cleq 2130  df-clel 2133

This theorem is referenced by:  6p5e11  9247  7p4e11  9250  8p3e11  9255  9p2e11  9261  fz1ssfz0  9890  fzo01  9986  bcp1nk  10501  arisum2  11261  ege2le3  11366  ef4p  11389  efgt1p2  11390  efgt1p  11391  ennnfonelem1  11909  dveflem  12844