Theorem 1e0p1 9425

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 9033	. 2 |- ( 0 + 1 ) = 1
2	1	eqcomi 2181	1 |- 1 = ( 0 + 1 )

Syntax hints:   = wceq 1353  (class class class)co 5875   0cc0 7811   1c1 7812   + caddc 7814

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 7904  ax-icn 7906  ax-addcl 7907  ax-mulcl 7909  ax-addcom 7911  ax-i2m1 7916  ax-0id 7919

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

This theorem is referenced by:  6p5e11  9456  7p4e11  9459  8p3e11  9464  9p2e11  9470  fz1ssfz0  10117  fz0to3un2pr  10123  fzo01  10216  bcp1nk  10742  arisum2  11507  ege2le3  11679  ef4p  11702  efgt1p2  11703  efgt1p  11704  prmdiv  12235  ennnfonelem1  12408  mulgnn0p1  12994  dveflem  14190  lgsdir2lem3  14434  lgseisenlem1  14453