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Theorem sbcbiVD 33777
Description: Implication form of sbcbiiOLD 3388. The following User's Proof is a Virtual Deduction proof completed automatically by the tools program completeusersproof.cmd, which invokes Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. sbcbi 33411 is sbcbiVD 33777 without virtual deductions and was automatically derived from sbcbiVD 33777.
 1:: 2:: 3:1,2: 4:1,3: 5:4: qed:5:
(Contributed by Alan Sare, 18-Mar-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
sbcbiVD

Proof of Theorem sbcbiVD
StepHypRef Expression
1 idn1 33452 . . . 4
2 idn2 33500 . . . . 5
3 spsbc 3340 . . . . 5
41, 2, 3e12 33622 . . . 4
5 sbcbig 3374 . . . . 5
65biimpd 207 . . . 4
71, 4, 6e12 33622 . . 3
87in2 33492 . 2
98in1 33449 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184  wal 1393   wcel 1819  wsbc 3327 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-12 1855  ax-13 2000  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111  df-sbc 3328  df-vd1 33448  df-vd2 33456 This theorem is referenced by: (None)
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