Theorem uun0.1 39005

Description: Convention notation form of un0.1 39006. (Contributed by Alan Sare, 23-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
uun0.1.1	|- ( T. -> ph )
uun0.1.2	|- ( ps -> ch )
uun0.1.3	|- ( ( T. /\ ps ) -> th )

Assertion

Ref	Expression
uun0.1	|- ( ps -> th )

Proof of Theorem uun0.1

Step	Hyp	Ref	Expression
1		tru 1487	. 2 |- T.
2		uun0.1.1	. . . . . 6 |- ( T. -> ph )
3		uun0.1.2	. . . . . 6 |- ( ps -> ch )
4	2, 3	pm3.2i 471	. . . . 5 |- ( ( T. -> ph ) /\ ( ps -> ch ) )
5		uun0.1.3	. . . . 5 |- ( ( T. /\ ps ) -> th )
6	4, 5	pm3.2i 471	. . . 4 |- ( ( ( T. -> ph ) /\ ( ps -> ch ) ) /\ ( ( T. /\ ps ) -> th ) )
7	6	simpri 478	. . 3 |- ( ( T. /\ ps ) -> th )
8	7	ex 450	. 2 |- ( T. -> ( ps -> th ) )
9	1, 8	ax-mp 5	1 |- ( ps -> th )

Syntax hints:   -> wi 4   /\ wa 384   T. wtru 1484

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

This theorem is referenced by:  un0.1  39006  sspwimp  39154