Theorem 1p1e2 8982

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 8924	. 2 |- 2 = ( 1 + 1 )
2	1	eqcomi 2174	1 |- ( 1 + 1 ) = 2

Syntax hints:   = wceq 1348  (class class class)co 5850   1c1 7762   + caddc 7764   2c2 8916

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 1440  ax-gen 1442  ax-ext 2152

This theorem depends on definitions:  df-bi 116  df-cleq 2163  df-2 8924

This theorem is referenced by:  2m1e1  8983  add1p1  9114  sub1m1  9115  nn0n0n1ge2  9269  3halfnz  9296  10p10e20  9424  5t4e20  9431  6t4e24  9435  7t3e21  9439  8t3e24  9445  9t3e27  9452  fz0to3un2pr  10066  fldiv4p1lem1div2  10248  m1modge3gt1  10314  fac2  10652  hash2  10734  nn0o1gt2  11851  3lcm2e6woprm  12027  logbleb  13594  logblt  13595  ex-exp  13683