Theorem problem1 35178

Description: Practice problem 1. Clues: 5p4e9 12374 3p2e5 12367 eqtri 2754 oveq1i 7415. (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 12367	. . 3 ⊢ (3 + 2) = 5
2	1	oveq1i 7415	. 2 ⊢ ((3 + 2) + 4) = (5 + 4)
3		5p4e9 12374	. 2 ⊢ (5 + 4) = 9
4	2, 3	eqtri 2754	1 ⊢ ((3 + 2) + 4) = 9

Syntax hints:   = wceq 1533  (class class class)co 7405   + caddc 11115  2c2 12271  3c3 12272  4c4 12273  5c5 12274  9c9 12278

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2697  ax-1cn 11170  ax-addcl 11172  ax-addass 11177

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2704  df-cleq 2718  df-clel 2804  df-rab 3427  df-v 3470  df-dif 3946  df-un 3948  df-in 3950  df-ss 3960  df-nul 4318  df-if 4524  df-sn 4624  df-pr 4626  df-op 4630  df-uni 4903  df-br 5142  df-iota 6489  df-fv 6545  df-ov 7408  df-2 12279  df-3 12280  df-4 12281  df-5 12282  df-6 12283  df-7 12284  df-8 12285  df-9 12286

This theorem is referenced by: (None)