Theorem 1e0p1 9515

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 9121	. 2 ⊢ (0 + 1) = 1
2	1	eqcomi 2200	1 ⊢ 1 = (0 + 1)

Syntax hints:   = wceq 1364  (class class class)co 5925  0cc0 7896  1c1 7897   + caddc 7899

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 1461  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-4 1524  ax-17 1540  ax-ial 1548  ax-ext 2178  ax-1cn 7989  ax-icn 7991  ax-addcl 7992  ax-mulcl 7994  ax-addcom 7996  ax-i2m1 8001  ax-0id 8004

This theorem depends on definitions:  df-bi 117  df-cleq 2189  df-clel 2192

This theorem is referenced by:  6p5e11  9546  7p4e11  9549  8p3e11  9554  9p2e11  9560  fz1ssfz0  10209  fz0to3un2pr  10215  fzo01  10309  bcp1nk  10871  arisum2  11681  ege2le3  11853  ef4p  11876  efgt1p2  11877  efgt1p  11878  bitsmod  12138  prmdiv  12428  ennnfonelem1  12649  mulgnn0p1  13339  dveflem  15046  lgsdir2lem3  15355  lgseisenlem1  15395