Theorem 1p1e2 9259

Description: 1 + 1 = 2. (Contributed by NM, 1-Apr-2008.)

Assertion

Ref	Expression
1p1e2	⊢ (1 + 1) = 2

Proof of Theorem 1p1e2

Step	Hyp	Ref	Expression
1		df-2 9201	. 2 ⊢ 2 = (1 + 1)
2	1	eqcomi 2235	1 ⊢ (1 + 1) = 2

Syntax hints:   = wceq 1397  (class class class)co 6017  1c1 8032   + caddc 8034  2c2 9193

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 1495  ax-gen 1497  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-cleq 2224  df-2 9201

This theorem is referenced by:  2m1e1  9260  add1p1  9393  sub1m1  9394  nn0n0n1ge2  9549  3halfnz  9576  10p10e20  9704  5t4e20  9711  6t4e24  9715  7t3e21  9719  8t3e24  9725  9t3e27  9732  fz0to3un2pr  10357  fldiv4p1lem1div2  10564  m1modge3gt1  10632  fac2  10992  hash2  11075  s2leng  11369  nn0o1gt2  12465  3lcm2e6woprm  12657  2exp8  13007  2exp11  13008  2exp16  13009  logbleb  15684  logblt  15685  1sgm2ppw  15718  1loopgrvd2fi  16155  2wlklem  16226  clwwlkext2edg  16272  ex-exp  16323