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Theorem ssoprab2i 6154
 Description: Inference of operation class abstraction subclass from implication. (Contributed by NM, 11-Nov-1995.) (Revised by David Abernethy, 19-Jun-2012.)
Hypothesis
Ref Expression
ssoprab2i.1
Assertion
Ref Expression
ssoprab2i
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,)   (,,)

Proof of Theorem ssoprab2i
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ssoprab2i.1 . . . . 5
21anim2i 553 . . . 4
322eximi 1586 . . 3
43ssopab2i 4474 . 2
5 dfoprab2 6113 . 2
6 dfoprab2 6113 . 2
74, 5, 63sstr4i 3379 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359  wex 1550   wceq 1652   wss 3312  cop 3809  copab 4257  coprab 6074 This theorem is referenced by:  sxbrsigalem5  24630 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-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-opab 4259  df-oprab 6077
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