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Theorem invdisj 4441
 Description: If there is a function ( ) such that ( )=x for all e. (x), then the sets (x) for distinct are disjoint. (Contributed by Mario Carneiro, 10-Dec-2016.)
Assertion
Ref Expression
invdisj
Distinct variable groups:   ,   ,   ,   ,

Proof of Theorem invdisj
StepHypRef Expression
1 nfra2 2844 . . 3
2 df-ral 2812 . . . . 5
3 rsp 2823 . . . . . . . . 9
4 eqcom 2466 . . . . . . . . 9
53, 4syl6ib 226 . . . . . . . 8
65imim2i 14 . . . . . . 7
76impd 431 . . . . . 6
87alimi 1633 . . . . 5
92, 8sylbi 195 . . . 4
10 mo2icl 3278 . . . 4
119, 10syl 16 . . 3
121, 11alrimi 1877 . 2
13 dfdisj2 4424 . 2
1412, 13sylibr 212 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  A.wal 1393  =wceq 1395  e.wcel 1818  E*wmo 2283  A.wral 2807  Disj_wdisj 4422 This theorem is referenced by:  disjxwrd  12680  ackbijnn  13640  incexc2  13650  itg1addlem1  22099  musum  23467  lgsquadlem1  23629  lgsquadlem2  23630  disjabrex  27443  disjabrexf  27444  phisum  31159 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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  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-ral 2812  df-rmo 2815  df-v 3111  df-disj 4423
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