Theorem 1e0p1 9419

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 9027	. 2 |- ( 0 + 1 ) = 1
2	1	eqcomi 2181	1 |- 1 = ( 0 + 1 )

Syntax hints:   = wceq 1353  (class class class)co 5870   0cc0 7806   1c1 7807   + caddc 7809

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 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-17 1526  ax-ial 1534  ax-ext 2159  ax-1cn 7899  ax-icn 7901  ax-addcl 7902  ax-mulcl 7904  ax-addcom 7906  ax-i2m1 7911  ax-0id 7914

This theorem depends on definitions:  df-bi 117  df-cleq 2170  df-clel 2173

This theorem is referenced by:  6p5e11  9450  7p4e11  9453  8p3e11  9458  9p2e11  9464  fz1ssfz0  10110  fz0to3un2pr  10116  fzo01  10209  bcp1nk  10733  arisum2  11498  ege2le3  11670  ef4p  11693  efgt1p2  11694  efgt1p  11695  prmdiv  12225  ennnfonelem1  12398  mulgnn0p1  12922  dveflem  13969  lgsdir2lem3  14213