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Theorem dropab2 27629
 Description: Theorem to aid use of the distinctor reduction theorem with ordered pair class abstraction. (Contributed by Andrew Salmon, 25-Jul-2011.)
Assertion
Ref Expression
dropab2

Proof of Theorem dropab2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 opeq2 3987 . . . . . . . 8
21sps 1771 . . . . . . 7
32eqeq2d 2449 . . . . . 6
43anbi1d 687 . . . . 5
54drex1 2060 . . . 4
65drex2 2061 . . 3
76abbidv 2552 . 2
8 df-opab 4269 . 2
9 df-opab 4269 . 2
107, 8, 93eqtr4g 2495 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360  wal 1550  wex 1551   wceq 1653  cab 2424  cop 3819  copab 4267 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-opab 4269
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