Theorem problem1 36554

Description: Practice problem 1. Clues: 5p4e9 12513 3p2e5 12506 eqtri 2786 oveq1i 7440. (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 12506	. . 3 ⊢ (3 + 2) = 5
2	1	oveq1i 7440	. 2 ⊢ ((3 + 2) + 4) = (5 + 4)
3		5p4e9 12513	. 2 ⊢ (5 + 4) = 9
4	2, 3	eqtri 2786	1 ⊢ ((3 + 2) + 4) = 9

This proof depends on syntax axioms:   = wceq 1569  (class class class)co 7430   + caddc 11216  2c2 12410  3c3 12411  4c4 12412  5c5 12413  9c9 12417

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1944  ax-6 2001  ax-7 2042  ax-8 2148  ax-9 2156  ax-ext 2735  ax-1cn 11271  ax-addcl 11273  ax-addass 11278

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1572  df-fal 1582  df-ex 1812  df-sb 2101  df-clab 2742  df-cleq 2755  df-clel 2839  df-rab 3417  df-v 3456  df-ss 3901  df-dif 4050  df-un 4154  df-nul 4282  df-if 4486  df-sn 4589  df-pr 4591  df-op 4839  df-uni 4871  df-br 5107  df-iota 6501  df-fv 6555  df-ov 7433  df-2 12418  df-3 12419  df-4 12420  df-5 12421  df-6 12422  df-7 12423  df-8 12424  df-9 12425

This theorem is used by: (None)