Theorem 1p1e2 9188

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 9130	. 2 ⊢ 2 = (1 + 1)
2	1	eqcomi 2211	1 ⊢ (1 + 1) = 2

Syntax hints:   = wceq 1373  (class class class)co 5967  1c1 7961   + caddc 7963  2c2 9122

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 1471  ax-gen 1473  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-cleq 2200  df-2 9130

This theorem is referenced by:  2m1e1  9189  add1p1  9322  sub1m1  9323  nn0n0n1ge2  9478  3halfnz  9505  10p10e20  9633  5t4e20  9640  6t4e24  9644  7t3e21  9648  8t3e24  9654  9t3e27  9661  fz0to3un2pr  10280  fldiv4p1lem1div2  10485  m1modge3gt1  10553  fac2  10913  hash2  10994  nn0o1gt2  12331  3lcm2e6woprm  12523  2exp8  12873  2exp11  12874  2exp16  12875  logbleb  15548  logblt  15549  1sgm2ppw  15582  ex-exp  15863