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Theorem re2luk3 1532
 Description: luk-3 1422 derived from Russell-Bernays'. This theorem, along with re1axmp 1529, re2luk1 1530, and re2luk2 1531 shows that rb-ax1 1517, rb-ax2 1518, rb-ax3 1519, and rb-ax4 1520, along with anmp 1516, 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 1515 . . . 4
21rblem7 1528 . . 3
3 rb-ax4 1520 . . . . . 6
4 rb-ax3 1519 . . . . . 6
53, 4rbsyl 1521 . . . . 5
6 rb-ax2 1518 . . . . 5
75, 6anmp 1516 . . . 4
8 rblem2 1523 . . . 4
97, 8anmp 1516 . . 3
102, 9rbsyl 1521 . 2
11 rb-imdf 1515 . . 3
1211rblem7 1528 . 2
1310, 12anmp 1516 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wo 357 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 177  df-or 359  df-an 360 This theorem is referenced by: (None)
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