Theorem 1e0p1 8981

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 8599	. 2 ⊢ (0 + 1) = 1
2	1	eqcomi 2093	1 ⊢ 1 = (0 + 1)

Syntax hints:   = wceq 1290  (class class class)co 5668  0cc0 7413  1c1 7414   + caddc 7416

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1382  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-4 1446  ax-17 1465  ax-ial 1473  ax-ext 2071  ax-1cn 7501  ax-icn 7503  ax-addcl 7504  ax-mulcl 7506  ax-addcom 7508  ax-i2m1 7513  ax-0id 7516

This theorem depends on definitions:  df-bi 116  df-cleq 2082  df-clel 2085

This theorem is referenced by:  6p5e11  9012  7p4e11  9015  8p3e11  9020  9p2e11  9026  fz1ssfz0  9594  fzo01  9690  bcp1nk  10233  arisum2  10956  ege2le3  11024  ef4p  11047  efgt1p2  11048  efgt1p  11049