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Theorem 7p2e9 7802
Description: 7 + 2 = 9. (Contributed by NM, 11-May-2004.)
Assertion
Ref Expression
7p2e9 (7 + 2) = 9

Proof of Theorem 7p2e9
StepHypRef Expression
1 df-2 7713 . . . . 5 2 = (1 + 1)
21oveq2i 5466 . . . 4 (7 + 2) = (7 + (1 + 1))
3 7cn 7739 . . . . 5 7
4 ax-1cn 6736 . . . . 5 1
53, 4, 4addassi 6793 . . . 4 ((7 + 1) + 1) = (7 + (1 + 1))
62, 5eqtr4i 2060 . . 3 (7 + 2) = ((7 + 1) + 1)
7 df-8 7719 . . . 4 8 = (7 + 1)
87oveq1i 5465 . . 3 (8 + 1) = ((7 + 1) + 1)
96, 8eqtr4i 2060 . 2 (7 + 2) = (8 + 1)
10 df-9 7720 . 2 9 = (8 + 1)
119, 10eqtr4i 2060 1 (7 + 2) = 9
Colors of variables: wff set class
Syntax hints:   = wceq 1242  (class class class)co 5455  1c1 6672   + caddc 6674  2c2 7704  7c7 7709  8c8 7710  9c9 7711
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-resscn 6735  ax-1cn 6736  ax-1re 6737  ax-addrcl 6740  ax-addass 6745
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-sn 3373  df-pr 3374  df-op 3376  df-uni 3572  df-br 3756  df-iota 4810  df-fv 4853  df-ov 5458  df-2 7713  df-3 7714  df-4 7715  df-5 7716  df-6 7717  df-7 7718  df-8 7719  df-9 7720
This theorem is referenced by:  7p3e10  7803  7t7e49  8190
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