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Theorem re2luk3 1585
 Description: luk-3 1475 derived from Russell-Bernays'. This theorem, along with re1axmp 1582, re2luk1 1583, and re2luk2 1584 shows that rb-ax1 1570, rb-ax2 1571, rb-ax3 1572, and rb-ax4 1573, along with anmp 1569, can be used as a complete axiomatization of propositional calculus. (Contributed by Anthony Hart, 19-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
re2luk3

Proof of Theorem re2luk3
StepHypRef Expression
1 rb-imdf 1568 . . . 4
21rblem7 1581 . . 3
3 rb-ax4 1573 . . . . . 6
4 rb-ax3 1572 . . . . . 6
53, 4rbsyl 1574 . . . . 5
6 rb-ax2 1571 . . . . 5
75, 6anmp 1569 . . . 4
8 rblem2 1576 . . . 4
97, 8anmp 1569 . . 3
102, 9rbsyl 1574 . 2
11 rb-imdf 1568 . . 3
1211rblem7 1581 . 2
1310, 12anmp 1569 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wo 368 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371 This theorem is referenced by: (None)
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