Theorem re1axmp 1689

Description: ax-mp 5 derived from Russell-Bernays'. (Contributed by Anthony Hart, 19-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
re1axmp.min	|- ph
re1axmp.maj	|- ( ph -> ps )

Assertion

Ref	Expression
re1axmp	|- ps

Proof of Theorem re1axmp

Step	Hyp	Ref	Expression
1		re1axmp.min	. 2 |- ph
2		re1axmp.maj	. . 3 |- ( ph -> ps )
3		rb-imdf 1675	. . . 4 |- -. ( -. ( -. ( ph -> ps ) \/ ( -. ph \/ ps ) ) \/ -. ( -. ( -. ph \/ ps ) \/ ( ph -> ps ) ) )
4	3	rblem6 1687	. . 3 |- ( -. ( ph -> ps ) \/ ( -. ph \/ ps ) )
5	2, 4	anmp 1676	. 2 |- ( -. ph \/ ps )
6	1, 5	anmp 1676	1 |- ps

Syntax hints:   -. wn 3   -> wi 4   \/ wo 383

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 197  df-or 385  df-an 386

This theorem is referenced by: (None)