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Theorem dedhb 3006
 Description: A deduction theorem for converting the inference => into a closed theorem. Use nfa1 1788 and nfab 2493 to eliminate the hypothesis of the substitution instance of the inference. For converting the inference form into a deduction form, abidnf 3005 is useful. (Contributed by NM, 8-Dec-2006.)
Hypotheses
Ref Expression
dedhb.1
dedhb.2
Assertion
Ref Expression
dedhb
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   (,)   ()

Proof of Theorem dedhb
StepHypRef Expression
1 dedhb.2 . 2
2 abidnf 3005 . . . 4
32eqcomd 2358 . . 3
4 dedhb.1 . . 3
53, 4syl 15 . 2
61, 5mpbiri 224 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176  wal 1540   wceq 1642   wcel 1710  cab 2339  wnfc 2476 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-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 This theorem is referenced by: (None)
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