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Theorem abrexco 5986
 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 2711 . . . . 5
2 vex 2959 . . . . . . . . 9
3 eqeq1 2442 . . . . . . . . . 10
43rexbidv 2726 . . . . . . . . 9
52, 4elab 3082 . . . . . . . 8
65anbi1i 677 . . . . . . 7
7 r19.41v 2861 . . . . . . 7
86, 7bitr4i 244 . . . . . 6
98exbii 1592 . . . . 5
101, 9bitri 241 . . . 4
11 rexcom4 2975 . . . 4
1210, 11bitr4i 244 . . 3
13 abrexco.1 . . . . 5
14 abrexco.2 . . . . . 6
1514eqeq2d 2447 . . . . 5
1613, 15ceqsexv 2991 . . . 4
1716rexbii 2730 . . 3
1812, 17bitri 241 . 2
1918abbii 2548 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359  wex 1550   wceq 1652   wcel 1725  cab 2422  wrex 2706  cvv 2956 This theorem is referenced by:  rankcf  8652  sylow1lem2  15233  sylow3lem1  15261  restco  17228 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 2417 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-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-rex 2711  df-v 2958
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