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Theorem brabsb 4468
 Description: The law of concretion in terms of substitutions. (Contributed by NM, 17-Mar-2008.)
Hypothesis
Ref Expression
brabsb.1
Assertion
Ref Expression
brabsb
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   (,)   ()   (,)

Proof of Theorem brabsb
StepHypRef Expression
1 df-br 4215 . 2
2 brabsb.1 . . 3
32eleq2i 2502 . 2
4 opelopabsb 4467 . 2
51, 3, 43bitri 264 1
 Colors of variables: wff set class Syntax hints:   wb 178   wceq 1653   wcel 1726  wsbc 3163  cop 3819   class class class wbr 4214  copab 4267 This theorem is referenced by:  eqerlem  6939 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-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332  ax-nul 4340  ax-pr 4405 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-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-sbc 3164  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-br 4215  df-opab 4269
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