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Theorem moop2 4747
 Description: "At most one" property of an ordered pair. (Contributed by NM, 11-Apr-2004.) (Revised by Mario Carneiro, 26-Apr-2015.)
Hypothesis
Ref Expression
moop2.1
Assertion
Ref Expression
moop2
Distinct variable group:   ,

Proof of Theorem moop2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eqtr2 2484 . . . 4
2 moop2.1 . . . . . 6
3 vex 3112 . . . . . 6
42, 3opth 4726 . . . . 5
54simprbi 464 . . . 4
61, 5syl 16 . . 3
76gen2 1619 . 2
8 nfcsb1v 3450 . . . . 5
9 nfcv 2619 . . . . 5
108, 9nfop 4233 . . . 4
1110nfeq2 2636 . . 3
12 csbeq1a 3443 . . . . 5
13 id 22 . . . . 5
1412, 13opeq12d 4225 . . . 4
1514eqeq2d 2471 . . 3
1611, 15mo4f 2336 . 2
177, 16mpbir 209 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  A.wal 1393  =wceq 1395  e.wcel 1818  E*wmo 2283   cvv 3109  [_csb 3434  <.cop 4035 This theorem is referenced by:  euop2  4752 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-rab 2816  df-v 3111  df-sbc 3328  df-csb 3435  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036
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