Theorem 1e0p1 9427

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 9035	. 2 ⊢ (0 + 1) = 1
2	1	eqcomi 2181	1 ⊢ 1 = (0 + 1)

Syntax hints:   = wceq 1353  (class class class)co 5877  0cc0 7813  1c1 7814   + caddc 7816

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 7906  ax-icn 7908  ax-addcl 7909  ax-mulcl 7911  ax-addcom 7913  ax-i2m1 7918  ax-0id 7921

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

This theorem is referenced by:  6p5e11  9458  7p4e11  9461  8p3e11  9466  9p2e11  9472  fz1ssfz0  10119  fz0to3un2pr  10125  fzo01  10218  bcp1nk  10744  arisum2  11509  ege2le3  11681  ef4p  11704  efgt1p2  11705  efgt1p  11706  prmdiv  12237  ennnfonelem1  12410  mulgnn0p1  12999  dveflem  14272  lgsdir2lem3  14516  lgseisenlem1  14535