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Theorem invdisj 4028
 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 2610 . . 3
2 df-ral 2561 . . . . 5
3 rsp 2616 . . . . . . . . 9
4 eqcom 2298 . . . . . . . . 9
53, 4syl6ib 217 . . . . . . . 8
65imim2i 13 . . . . . . 7
76imp3a 420 . . . . . 6
87alimi 1549 . . . . 5
92, 8sylbi 187 . . . 4
10 mo2icl 2957 . . . 4
119, 10syl 15 . . 3
121, 11alrimi 1757 . 2
13 df-disj 4010 . . 3 Disj
14 df-rmo 2564 . . . 4
1514albii 1556 . . 3
1613, 15bitri 240 . 2 Disj
1712, 16sylibr 203 1 Disj
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358  wal 1530   wceq 1632   wcel 1696  wmo 2157  wral 2556  wrmo 2559  Disj wdisj 4009 This theorem is referenced by:  ackbijnn  12302  incexc2  12313  itg1addlem1  19063  musum  20447  lgsquadlem1  20609  lgsquadlem2  20610  disjabrex  23374  disjabrexf  23375  phisum  27621 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rmo 2564  df-v 2803  df-disj 4010
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