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Theorem brabsbOLD 4466
 Description: The law of concretion in terms of substitutions. (Contributed by NM, 17-Mar-2008.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
brabsbOLD.1
Assertion
Ref Expression
brabsbOLD
Distinct variable groups:   ,,   ,,
Allowed substitution hints:   (,,,)   (,,,)

Proof of Theorem brabsbOLD
StepHypRef Expression
1 brabsbOLD.1 . . 3
21breqi 4220 . 2
3 df-br 4215 . 2
4 opelopabsbOLD 4465 . 2
52, 3, 43bitri 264 1
 Colors of variables: wff set class Syntax hints:   wb 178   wceq 1653  wsb 1659   wcel 1726  cop 3819   class class class wbr 4214  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-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-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  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-br 4215  df-opab 4269
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