Theorem imsym1 32417

Description: A symmetry with ->.

See negsym1 32416 for more information. (Contributed by Anthony Hart, 4-Sep-2011.)

Assertion

Ref	Expression
imsym1	|- ( ( ps -> ( ps -> F. ) ) -> ( ps -> ph ) )

Proof of Theorem imsym1

Step	Hyp	Ref	Expression
1		pm2.21 120	. 2 |- ( -. ps -> ( ps -> ph ) )
2		falim 1498	. . 3 |- ( F. -> ph )
3	2	imim2i 16	. 2 |- ( ( ps -> F. ) -> ( ps -> ph ) )
4	1, 3	ja 173	1 |- ( ( ps -> ( ps -> F. ) ) -> ( ps -> ph ) )

Syntax hints:   -> wi 4   F. wfal 1488

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-tru 1486  df-fal 1489

This theorem is referenced by: (None)