Theorem un01 39016

Description: A unionizing deduction. (Contributed by Alan Sare, 28-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
un01.1	|- (. (. T. ,. ph ). ->. ps ).

Assertion

Ref	Expression
un01	|- (. ph ->. ps ).

Proof of Theorem un01

Step	Hyp	Ref	Expression
1		tru 1487	. . . 4 |- T.
2	1	jctl 564	. . 3 |- ( ph -> ( T. /\ ph ) )
3		un01.1	. . . 4 |- (. (. T. ,. ph ). ->. ps ).
4	3	dfvd2ani 38799	. . 3 |- ( ( T. /\ ph ) -> ps )
5	2, 4	syl 17	. 2 |- ( ph -> ps )
6	5	dfvd1ir 38789	1 |- (. ph ->. ps ).

Syntax hints:   /\ wa 384   T. wtru 1484   (.wvd1 38785   (.wvhc2 38796

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-vd1 38786  df-vhc2 38797

This theorem is referenced by: (None)