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Theorem 5p2e7 9131
Description: 5 + 2 = 7. (Contributed by NM, 11-May-2004.)
Assertion
Ref Expression
5p2e7 (5 + 2) = 7

Proof of Theorem 5p2e7
StepHypRef Expression
1 df-2 9043 . . . . 5 2 = (1 + 1)
21oveq2i 5930 . . . 4 (5 + 2) = (5 + (1 + 1))
3 5cn 9064 . . . . 5 5 ∈ ℂ
4 ax-1cn 7967 . . . . 5 1 ∈ ℂ
53, 4, 4addassi 8029 . . . 4 ((5 + 1) + 1) = (5 + (1 + 1))
62, 5eqtr4i 2217 . . 3 (5 + 2) = ((5 + 1) + 1)
7 df-6 9047 . . . 4 6 = (5 + 1)
87oveq1i 5929 . . 3 (6 + 1) = ((5 + 1) + 1)
96, 8eqtr4i 2217 . 2 (5 + 2) = (6 + 1)
10 df-7 9048 . 2 7 = (6 + 1)
119, 10eqtr4i 2217 1 (5 + 2) = 7
Colors of variables: wff set class
Syntax hints:   = wceq 1364  (class class class)co 5919  1c1 7875   + caddc 7877  2c2 9035  5c5 9038  6c6 9039  7c7 9040
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175  ax-resscn 7966  ax-1cn 7967  ax-1re 7968  ax-addrcl 7971  ax-addass 7976
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-rex 2478  df-v 2762  df-un 3158  df-in 3160  df-ss 3167  df-sn 3625  df-pr 3626  df-op 3628  df-uni 3837  df-br 4031  df-iota 5216  df-fv 5263  df-ov 5922  df-2 9043  df-3 9044  df-4 9045  df-5 9046  df-6 9047  df-7 9048
This theorem is referenced by:  5p3e8  9132
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