Theorem problem1 32908

Description: Practice problem 1. Clues: 5p4e9 11796 3p2e5 11789 eqtri 2844 oveq1i 7166. (Contributed by Filip Cernatescu, 16-Mar-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
problem1	⊢ ((3 + 2) + 4) = 9

Proof of Theorem problem1

Step	Hyp	Ref	Expression
1		3p2e5 11789	. . 3 ⊢ (3 + 2) = 5
2	1	oveq1i 7166	. 2 ⊢ ((3 + 2) + 4) = (5 + 4)
3		5p4e9 11796	. 2 ⊢ (5 + 4) = 9
4	2, 3	eqtri 2844	1 ⊢ ((3 + 2) + 4) = 9

Syntax hints:   = wceq 1537  (class class class)co 7156   + caddc 10540  2c2 11693  3c3 11694  4c4 11695  5c5 11696  9c9 11700

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2177  ax-ext 2793  ax-1cn 10595  ax-addcl 10597  ax-addass 10602

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3an 1085  df-tru 1540  df-ex 1781  df-nf 1785  df-sb 2070  df-clab 2800  df-cleq 2814  df-clel 2893  df-nfc 2963  df-rab 3147  df-v 3496  df-dif 3939  df-un 3941  df-in 3943  df-ss 3952  df-nul 4292  df-if 4468  df-sn 4568  df-pr 4570  df-op 4574  df-uni 4839  df-br 5067  df-iota 6314  df-fv 6363  df-ov 7159  df-2 11701  df-3 11702  df-4 11703  df-5 11704  df-6 11705  df-7 11706  df-8 11707  df-9 11708

This theorem is referenced by: (None)