Theorem 1p1e2 9101

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 9043	. 2 ⊢ 2 = (1 + 1)
2	1	eqcomi 2197	1 ⊢ (1 + 1) = 2

Syntax hints:   = wceq 1364  (class class class)co 5919  1c1 7875   + caddc 7877  2c2 9035

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 1458  ax-gen 1460  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-cleq 2186  df-2 9043

This theorem is referenced by:  2m1e1  9102  add1p1  9235  sub1m1  9236  nn0n0n1ge2  9390  3halfnz  9417  10p10e20  9545  5t4e20  9552  6t4e24  9556  7t3e21  9560  8t3e24  9566  9t3e27  9573  fz0to3un2pr  10192  fldiv4p1lem1div2  10377  m1modge3gt1  10445  fac2  10805  hash2  10886  nn0o1gt2  12049  3lcm2e6woprm  12227  logbleb  15134  logblt  15135  ex-exp  15289