Theorem rb-ax2 1518

Description: The second of four axioms in the Russell-Bernays axiom system. (Contributed by Anthony Hart, 13-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
rb-ax2	|- (-. (ph \/ ps) \/ (ps \/ ph))

Proof of Theorem rb-ax2

Step	Hyp	Ref	Expression
1		pm1.4 375	. . . 4 |- ((ph \/ ps) -> (ps \/ ph))
2	1	con3i 127	. . 3 |- (-. (ps \/ ph) -> -. (ph \/ ps))
3	2	con1i 121	. 2 |- (-. -. (ph \/ ps) -> (ps \/ ph))
4	3	orri 365	1 |- (-. (ph \/ ps) \/ (ps \/ ph))

Syntax hints:  -. wn 3   \/ wo 357

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 177  df-or 359

This theorem is referenced by:  rblem1  1522  rblem2  1523  rblem3  1524  rblem4  1525  rblem5  1526  rblem6  1527  re2luk1  1530  re2luk2  1531  re2luk3  1532