MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  7p3e10OLD Structured version   Visualization version   GIF version

Theorem 7p3e10OLD 11211
Description: 7 + 3 = 10. (Contributed by NM, 5-Feb-2007.) Obsolete version of 7p3e10 11641 as of 8-Sep-2021. (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
7p3e10OLD (7 + 3) = 10

Proof of Theorem 7p3e10OLD
StepHypRef Expression
1 df-3 11118 . . . 4 3 = (2 + 1)
21oveq2i 6701 . . 3 (7 + 3) = (7 + (2 + 1))
3 7cn 11142 . . . 4 7 ∈ ℂ
4 2cn 11129 . . . 4 2 ∈ ℂ
5 ax-1cn 10032 . . . 4 1 ∈ ℂ
63, 4, 5addassi 10086 . . 3 ((7 + 2) + 1) = (7 + (2 + 1))
72, 6eqtr4i 2676 . 2 (7 + 3) = ((7 + 2) + 1)
8 df-10OLD 11125 . . 3 10 = (9 + 1)
9 7p2e9 11210 . . . 4 (7 + 2) = 9
109oveq1i 6700 . . 3 ((7 + 2) + 1) = (9 + 1)
118, 10eqtr4i 2676 . 2 10 = ((7 + 2) + 1)
127, 11eqtr4i 2676 1 (7 + 3) = 10
Colors of variables: wff setvar class
Syntax hints:   = wceq 1523  (class class class)co 6690  1c1 9975   + caddc 9977  2c2 11108  3c3 11109  7c7 11113  9c9 11115  10c10 11116
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631  ax-resscn 10031  ax-1cn 10032  ax-icn 10033  ax-addcl 10034  ax-addrcl 10035  ax-mulcl 10036  ax-mulrcl 10037  ax-addass 10039  ax-i2m1 10042  ax-1ne0 10043  ax-rrecex 10046  ax-cnre 10047
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1056  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-ne 2824  df-ral 2946  df-rex 2947  df-rab 2950  df-v 3233  df-dif 3610  df-un 3612  df-in 3614  df-ss 3621  df-nul 3949  df-if 4120  df-sn 4211  df-pr 4213  df-op 4217  df-uni 4469  df-br 4686  df-iota 5889  df-fv 5934  df-ov 6693  df-2 11117  df-3 11118  df-4 11119  df-5 11120  df-6 11121  df-7 11122  df-8 11123  df-9 11124  df-10OLD 11125
This theorem is referenced by:  7p3e10bOLD  11642  7p4e11OLD  11644
  Copyright terms: Public domain W3C validator