Theorem problem1 35310

Description: Practice problem 1. Clues: 5p4e9 12410 3p2e5 12403 eqtri 2756 oveq1i 7436. (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 12403	. . 3 ⊢ (3 + 2) = 5
2	1	oveq1i 7436	. 2 ⊢ ((3 + 2) + 4) = (5 + 4)
3		5p4e9 12410	. 2 ⊢ (5 + 4) = 9
4	2, 3	eqtri 2756	1 ⊢ ((3 + 2) + 4) = 9

Syntax hints:   = wceq 1533  (class class class)co 7426   + caddc 11151  2c2 12307  3c3 12308  4c4 12309  5c5 12310  9c9 12314

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 2699  ax-1cn 11206  ax-addcl 11208  ax-addass 11213

This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2706  df-cleq 2720  df-clel 2806  df-rab 3431  df-v 3475  df-dif 3952  df-un 3954  df-in 3956  df-ss 3966  df-nul 4327  df-if 4533  df-sn 4633  df-pr 4635  df-op 4639  df-uni 4913  df-br 5153  df-iota 6505  df-fv 6561  df-ov 7429  df-2 12315  df-3 12316  df-4 12317  df-5 12318  df-6 12319  df-7 12320  df-8 12321  df-9 12322

This theorem is referenced by: (None)