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Theorem 5p2e7 9051
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 8964 . . . . 5 2 = (1 + 1)
21oveq2i 5880 . . . 4 (5 + 2) = (5 + (1 + 1))
3 5cn 8985 . . . . 5 5 ∈ ℂ
4 ax-1cn 7892 . . . . 5 1 ∈ ℂ
53, 4, 4addassi 7953 . . . 4 ((5 + 1) + 1) = (5 + (1 + 1))
62, 5eqtr4i 2201 . . 3 (5 + 2) = ((5 + 1) + 1)
7 df-6 8968 . . . 4 6 = (5 + 1)
87oveq1i 5879 . . 3 (6 + 1) = ((5 + 1) + 1)
96, 8eqtr4i 2201 . 2 (5 + 2) = (6 + 1)
10 df-7 8969 . 2 7 = (6 + 1)
119, 10eqtr4i 2201 1 (5 + 2) = 7
Colors of variables: wff set class
Syntax hints:   = wceq 1353  (class class class)co 5869  1c1 7800   + caddc 7802  2c2 8956  5c5 8959  6c6 8960  7c7 8961
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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159  ax-resscn 7891  ax-1cn 7892  ax-1re 7893  ax-addrcl 7896  ax-addass 7901
This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-rex 2461  df-v 2739  df-un 3133  df-in 3135  df-ss 3142  df-sn 3597  df-pr 3598  df-op 3600  df-uni 3808  df-br 4001  df-iota 5174  df-fv 5220  df-ov 5872  df-2 8964  df-3 8965  df-4 8966  df-5 8967  df-6 8968  df-7 8969
This theorem is referenced by:  5p3e8  9052
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