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Theorem abrexco 5463
 Description: Composition of two image maps and . (Contributed by set.mm contributors, 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 2620 . . . 4
2 vex 2862 . . . . . . . 8
3 eqeq1 2359 . . . . . . . . 9
43rexbidv 2635 . . . . . . . 8
52, 4elab 2985 . . . . . . 7
65anbi1i 676 . . . . . 6
7 r19.41v 2764 . . . . . 6
86, 7bitr4i 243 . . . . 5
98exbii 1582 . . . 4
101, 9bitri 240 . . 3
11 rexcom4 2878 . . 3
12 abrexco.1 . . . . 5
13 abrexco.2 . . . . . 6
1413eqeq2d 2364 . . . . 5
1512, 14ceqsexv 2894 . . . 4
1615rexbii 2639 . . 3
1710, 11, 163bitr2i 264 . 2
1817abbii 2465 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 358  wex 1541   wceq 1642   wcel 1710  cab 2339  wrex 2615  cvv 2859 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rex 2620  df-v 2861 This theorem is referenced by: (None)
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