Theorem 1p1e2 9227

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 9169	. 2 ⊢ 2 = (1 + 1)
2	1	eqcomi 2233	1 ⊢ (1 + 1) = 2

Syntax hints:   = wceq 1395  (class class class)co 6001  1c1 8000   + caddc 8002  2c2 9161

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 1493  ax-gen 1495  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-cleq 2222  df-2 9169

This theorem is referenced by:  2m1e1  9228  add1p1  9361  sub1m1  9362  nn0n0n1ge2  9517  3halfnz  9544  10p10e20  9672  5t4e20  9679  6t4e24  9683  7t3e21  9687  8t3e24  9693  9t3e27  9700  fz0to3un2pr  10319  fldiv4p1lem1div2  10525  m1modge3gt1  10593  fac2  10953  hash2  11034  s2leng  11321  nn0o1gt2  12416  3lcm2e6woprm  12608  2exp8  12958  2exp11  12959  2exp16  12960  logbleb  15635  logblt  15636  1sgm2ppw  15669  ex-exp  16091