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Theorem dedhb 2948
 Description: A deduction theorem for converting the inference => into a closed theorem. Use nfa1 1768 and nfab 2436 to eliminate the hypothesis of the substitution instance of the inference. For converting the inference form into a deduction form, abidnf 2947 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 2947 . . . 4
32eqcomd 2301 . . 3
4 dedhb.1 . . 3
53, 4syl 15 . 2
61, 5mpbiri 224 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176  wal 1530   wceq 1632   wcel 1696  cab 2282  wnfc 2419 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421
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