Theorem problem1 35645

Description: Practice problem 1. Clues: 5p4e9 12315 3p2e5 12308 eqtri 2752 oveq1i 7379. (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 12308	. . 3 ⊢ (3 + 2) = 5
2	1	oveq1i 7379	. 2 ⊢ ((3 + 2) + 4) = (5 + 4)
3		5p4e9 12315	. 2 ⊢ (5 + 4) = 9
4	2, 3	eqtri 2752	1 ⊢ ((3 + 2) + 4) = 9

Syntax hints:   = wceq 1540  (class class class)co 7369   + caddc 11047  2c2 12217  3c3 12218  4c4 12219  5c5 12220  9c9 12224

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2701  ax-1cn 11102  ax-addcl 11104  ax-addass 11109

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-rab 3403  df-v 3446  df-dif 3914  df-un 3916  df-ss 3928  df-nul 4293  df-if 4485  df-sn 4586  df-pr 4588  df-op 4592  df-uni 4868  df-br 5103  df-iota 6452  df-fv 6507  df-ov 7372  df-2 12225  df-3 12226  df-4 12227  df-5 12228  df-6 12229  df-7 12230  df-8 12231  df-9 12232

This theorem is referenced by: (None)