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Theorem invdisj 4193
 Description: If there is a function such that for all , then the sets for distinct are disjoint. (Contributed by Mario Carneiro, 10-Dec-2016.)
Assertion
Ref Expression
invdisj Disj
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem invdisj
StepHypRef Expression
1 nfra2 2752 . . 3
2 df-ral 2702 . . . . 5
3 rsp 2758 . . . . . . . . 9
4 eqcom 2437 . . . . . . . . 9
53, 4syl6ib 218 . . . . . . . 8
65imim2i 14 . . . . . . 7
76imp3a 421 . . . . . 6
87alimi 1568 . . . . 5
92, 8sylbi 188 . . . 4
10 mo2icl 3105 . . . 4
119, 10syl 16 . . 3
121, 11alrimi 1781 . 2
13 dfdisj2 4176 . 2 Disj
1412, 13sylibr 204 1 Disj
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359  wal 1549   wceq 1652   wcel 1725  wmo 2281  wral 2697  Disj wdisj 4174 This theorem is referenced by:  ackbijnn  12599  incexc2  12610  itg1addlem1  19576  musum  20968  lgsquadlem1  21130  lgsquadlem2  21131  disjabrex  24016  disjabrexf  24017  phisum  27486 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rmo 2705  df-v 2950  df-disj 4175
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