Theorem 3p1e4 9440

Description: 3 + 1 = 4. (Contributed by Mario Carneiro, 18-Apr-2015.)

Assertion

Ref	Expression
3p1e4	|- ( 3 + 1 ) = 4

Proof of Theorem 3p1e4

Step	Hyp	Ref	Expression
1		df-4 9365	. 2 |- 4 = ( 3 + 1 )
2	1	eqcomi 2242	1 |- ( 3 + 1 ) = 4

This proof depends on syntax axioms:   = wceq 1402  (class class class)co 6085   1c1 8180   + caddc 8182   3c3 9356   4c4 9357

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1500  ax-gen 1502  ax-ext 2220

This proof depends on definitions:  df-bi 117  df-cleq 2231  df-4 9365

This theorem is used by:  7t6e42  9889  8t5e40  9894  9t5e45  9901  fac4  11171  4bc3eq4  11212  hash4  11255  2exp16  13216  cosq23lt0  15934  binom4  16081  log2ublem3  16085  log2ublog2  16086