Theorem 1e0p1 9547

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 9152	. 2 |- ( 0 + 1 ) = 1
2	1	eqcomi 2209	1 |- 1 = ( 0 + 1 )

Syntax hints:   = wceq 1373  (class class class)co 5946   0cc0 7927   1c1 7928   + caddc 7930

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 1470  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-4 1533  ax-17 1549  ax-ial 1557  ax-ext 2187  ax-1cn 8020  ax-icn 8022  ax-addcl 8023  ax-mulcl 8025  ax-addcom 8027  ax-i2m1 8032  ax-0id 8035

This theorem depends on definitions:  df-bi 117  df-cleq 2198  df-clel 2201

This theorem is referenced by:  6p5e11  9578  7p4e11  9581  8p3e11  9586  9p2e11  9592  fz1ssfz0  10241  fz0to3un2pr  10247  fzo01  10347  bcp1nk  10909  pfx1  11157  arisum2  11843  ege2le3  12015  ef4p  12038  efgt1p2  12039  efgt1p  12040  bitsmod  12300  prmdiv  12590  ennnfonelem1  12811  mulgnn0p1  13502  dveflem  15231  lgsdir2lem3  15540  lgseisenlem1  15580