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Theorem rblem4 1534
 Description: Used to rederive the Lukasiewicz axioms from Russell-Bernays'. (Contributed by Anthony Hart, 18-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
rblem4.1
rblem4.2
rblem4.3
Assertion
Ref Expression
rblem4

Proof of Theorem rblem4
StepHypRef Expression
1 rblem4.3 . . . 4
2 rblem4.2 . . . 4
31, 2rblem1 1531 . . 3
4 rblem4.1 . . 3
53, 4rblem1 1531 . 2
6 rb-ax2 1527 . . . 4
7 rb-ax2 1527 . . . . . 6
8 rb-ax1 1526 . . . . . 6
97, 8anmp 1525 . . . . 5
10 rb-ax2 1527 . . . . 5
119, 10rbsyl 1530 . . . 4
126, 11rbsyl 1530 . . 3
13 rb-ax4 1529 . . . 4
14 rb-ax2 1527 . . . . . 6
15 rblem2 1532 . . . . . 6
1614, 15rbsyl 1530 . . . . 5
17 rb-ax3 1528 . . . . . 6
18 rblem2 1532 . . . . . 6
1917, 18anmp 1525 . . . . 5
2016, 19rblem1 1531 . . . 4
2113, 20rbsyl 1530 . . 3
2212, 21rbsyl 1530 . 2
235, 22rbsyl 1530 1
 Colors of variables: wff set class Syntax hints:   wn 3   wo 358 This theorem is referenced by:  re2luk1  1539 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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