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Theorem re2luk3 1541
 Description: luk-3 1431 derived from Russell-Bernays'. This theorem, along with re1axmp 1538, re2luk1 1539, and re2luk2 1540 shows that rb-ax1 1526, rb-ax2 1527, rb-ax3 1528, and rb-ax4 1529, along with anmp 1525, 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 1524 . . . 4
21rblem7 1537 . . 3
3 rb-ax4 1529 . . . . . 6
4 rb-ax3 1528 . . . . . 6
53, 4rbsyl 1530 . . . . 5
6 rb-ax2 1527 . . . . 5
75, 6anmp 1525 . . . 4
8 rblem2 1532 . . . 4
97, 8anmp 1525 . . 3
102, 9rbsyl 1530 . 2
11 rb-imdf 1524 . . 3
1211rblem7 1537 . 2
1310, 12anmp 1525 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wo 358 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361
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