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Theorem abrexco 6149
 Description: Composition of two image maps and . (Contributed by NM, 27-May-2013.)
Hypotheses
Ref Expression
abrexco.1
abrexco.2
Assertion
Ref Expression
abrexco
Distinct variable groups:   ,,   ,,   ,   ,   ,,   ,
Allowed substitution hints:   (,)   (,)   (,,)   (,,)

Proof of Theorem abrexco
StepHypRef Expression
1 df-rex 2743 . . . . 5
2 vex 3048 . . . . . . . . 9
3 eqeq1 2455 . . . . . . . . . 10
43rexbidv 2901 . . . . . . . . 9
52, 4elab 3185 . . . . . . . 8
65anbi1i 701 . . . . . . 7
7 r19.41v 2942 . . . . . . 7
86, 7bitr4i 256 . . . . . 6
98exbii 1718 . . . . 5
101, 9bitri 253 . . . 4
11 rexcom4 3067 . . . 4
1210, 11bitr4i 256 . . 3
13 abrexco.1 . . . . 5
14 abrexco.2 . . . . . 6
1514eqeq2d 2461 . . . . 5
1613, 15ceqsexv 3084 . . . 4
1716rexbii 2889 . . 3
1812, 17bitri 253 . 2
1918abbii 2567 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 371   wceq 1444  wex 1663   wcel 1887  cab 2437  wrex 2738  cvv 3045 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-ral 2742  df-rex 2743  df-v 3047 This theorem is referenced by:  rankcf  9202  sylow1lem2  17251  sylow3lem1  17279  restco  20180
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