Theorem simplbi2comtVD 39124

Description: Virtual deduction proof of simplbi2comt 656. The following User's Proof is a Virtual Deduction proof completed automatically by the tools program completeusersproof.cmd, which invokes Mel L. O'Cat's mmj2 and Norm Megill's Metamath Proof Assistant. simplbi2comt 656 is simplbi2comtVD 39124 without virtual deductions and was automatically derived from simplbi2comtVD 39124.

1::	|- (. ( ph <-> ( ps /\ ch ) ) ->. ( ph <-> ( ps /\ ch ) ) ).
2:1:	|- (. ( ph <-> ( ps /\ ch ) ) ->. ( ( ps /\ ch ) -> ph ) ).
3:2:	|- (. ( ph <-> ( ps /\ ch ) ) ->. ( ps -> ( ch -> ph ) ) ).
4:3:	|- (. ( ph <-> ( ps /\ ch ) ) ->. ( ch -> ( ps -> ph ) ) ).
qed:4:	|- ( ( ph <-> ( ps /\ ch ) ) -> ( ch -> ( ps -> ph ) ) )

(Contributed by Alan Sare, 22-Jul-2012.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
simplbi2comtVD	|- ( ( ph <-> ( ps /\ ch ) ) -> ( ch -> ( ps -> ph ) ) )

Proof of Theorem simplbi2comtVD

Step	Hyp	Ref	Expression
1		idn1 38790	. . . . 5 |- (. ( ph <-> ( ps /\ ch ) ) ->. ( ph <-> ( ps /\ ch ) ) ).
2		biimpr 210	. . . . 5 |- ( ( ph <-> ( ps /\ ch ) ) -> ( ( ps /\ ch ) -> ph ) )
3	1, 2	e1a 38852	. . . 4 |- (. ( ph <-> ( ps /\ ch ) ) ->. ( ( ps /\ ch ) -> ph ) ).
4		pm3.3 460	. . . 4 |- ( ( ( ps /\ ch ) -> ph ) -> ( ps -> ( ch -> ph ) ) )
5	3, 4	e1a 38852	. . 3 |- (. ( ph <-> ( ps /\ ch ) ) ->. ( ps -> ( ch -> ph ) ) ).
6		pm2.04 90	. . 3 |- ( ( ps -> ( ch -> ph ) ) -> ( ch -> ( ps -> ph ) ) )
7	5, 6	e1a 38852	. 2 |- (. ( ph <-> ( ps /\ ch ) ) ->. ( ch -> ( ps -> ph ) ) ).
8	7	in1 38787	1 |- ( ( ph <-> ( ps /\ ch ) ) -> ( ch -> ( ps -> ph ) ) )

Syntax hints:   -> wi 4   <-> wb 196   /\ wa 384

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-vd1 38786

This theorem is referenced by: (None)