Theorem consym1 32419

Description: A symmetry with /\.

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

Assertion

Ref	Expression
consym1	|- ( ( ps /\ ( ps /\ F. ) ) -> ( ps /\ ph ) )

Proof of Theorem consym1

Step	Hyp	Ref	Expression
1		falim 1498	. . 3 |- ( F. -> ( ( ps /\ ( ps /\ F. ) ) -> ( ps /\ ph ) ) )
2	1	ad2antll 765	. 2 |- ( ( ps /\ ( ps /\ F. ) ) -> ( ( ps /\ ( ps /\ F. ) ) -> ( ps /\ ph ) ) )
3	2	pm2.43i 52	1 |- ( ( ps /\ ( ps /\ F. ) ) -> ( ps /\ ph ) )

Syntax hints:   -> wi 4   /\ wa 384   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-an 386  df-tru 1486  df-fal 1489

This theorem is referenced by: (None)