Theorem problem1 35808

Description: Practice problem 1. Clues: 5p4e9 12296 3p2e5 12289 eqtri 2757 oveq1i 7366. (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 12289	. . 3 ⊢ (3 + 2) = 5
2	1	oveq1i 7366	. 2 ⊢ ((3 + 2) + 4) = (5 + 4)
3		5p4e9 12296	. 2 ⊢ (5 + 4) = 9
4	2, 3	eqtri 2757	1 ⊢ ((3 + 2) + 4) = 9

Syntax hints:   = wceq 1541  (class class class)co 7356   + caddc 11027  2c2 12198  3c3 12199  4c4 12200  5c5 12201  9c9 12205

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 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2706  ax-1cn 11082  ax-addcl 11084  ax-addass 11089

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2713  df-cleq 2726  df-clel 2809  df-rab 3398  df-v 3440  df-dif 3902  df-un 3904  df-ss 3916  df-nul 4284  df-if 4478  df-sn 4579  df-pr 4581  df-op 4585  df-uni 4862  df-br 5097  df-iota 6446  df-fv 6498  df-ov 7359  df-2 12206  df-3 12207  df-4 12208  df-5 12209  df-6 12210  df-7 12211  df-8 12212  df-9 12213

This theorem is referenced by: (None)