Theorem uunT1p1 39008

Description: A deduction unionizing a non-unionized collection of virtual hypotheses. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
uunT1p1.1	|- ( ( ph /\ T. ) -> ps )

Assertion

Ref	Expression
uunT1p1	|- ( ph -> ps )

Proof of Theorem uunT1p1

Step	Hyp	Ref	Expression
1		ancom 466	. . 3 |- ( ( ph /\ T. ) <-> ( T. /\ ph ) )
2		truan 1501	. . 3 |- ( ( T. /\ ph ) <-> ph )
3	1, 2	bitri 264	. 2 |- ( ( ph /\ T. ) <-> ph )
4		uunT1p1.1	. 2 |- ( ( ph /\ T. ) -> ps )
5	3, 4	sylbir 225	1 |- ( ph -> ps )

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: (None)