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Theorem dedhb 2853
 Description: A deduction theorem for converting the inference => into a closed theorem. Use nfa1 1521 and nfab 2286 to eliminate the hypothesis of the substitution instance of the inference. For converting the inference form into a deduction form, abidnf 2852 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 2852 . . . 4
32eqcomd 2145 . . 3
4 dedhb.1 . . 3
53, 4syl 14 . 2
61, 5mpbiri 167 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104  wal 1329   wceq 1331   wcel 1480  cab 2125  wnfc 2268 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270 This theorem is referenced by: (None)
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