Theorem 1e0p1 9223

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 8834	. 2 ⊢ (0 + 1) = 1
2	1	eqcomi 2143	1 ⊢ 1 = (0 + 1)

Syntax hints:   = wceq 1331  (class class class)co 5774  0cc0 7620  1c1 7621   + caddc 7623

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-17 1506  ax-ial 1514  ax-ext 2121  ax-1cn 7713  ax-icn 7715  ax-addcl 7716  ax-mulcl 7718  ax-addcom 7720  ax-i2m1 7725  ax-0id 7728

This theorem depends on definitions:  df-bi 116  df-cleq 2132  df-clel 2135

This theorem is referenced by:  6p5e11  9254  7p4e11  9257  8p3e11  9262  9p2e11  9268  fz1ssfz0  9897  fzo01  9993  bcp1nk  10508  arisum2  11268  ege2le3  11377  ef4p  11400  efgt1p2  11401  efgt1p  11402  ennnfonelem1  11920  dveflem  12855