Theorem bnj951 30846

Description: /\-manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Hypotheses

Ref	Expression
bnj951.1	|- ( ta -> ph )
bnj951.2	|- ( ta -> ps )
bnj951.3	|- ( ta -> ch )
bnj951.4	|- ( ta -> th )

Assertion

Ref	Expression
bnj951	|- ( ta -> ( ph /\ ps /\ ch /\ th ) )

Proof of Theorem bnj951

Step	Hyp	Ref	Expression
1		bnj951.1	. . 3 |- ( ta -> ph )
2		bnj951.2	. . 3 |- ( ta -> ps )
3		bnj951.3	. . 3 |- ( ta -> ch )
4	1, 2, 3	3jca 1242	. 2 |- ( ta -> ( ph /\ ps /\ ch ) )
5		bnj951.4	. 2 |- ( ta -> th )
6		df-bnj17 30753	. 2 |- ( ( ph /\ ps /\ ch /\ th ) <-> ( ( ph /\ ps /\ ch ) /\ th ) )
7	4, 5, 6	sylanbrc 698	1 |- ( ta -> ( ph /\ ps /\ ch /\ th ) )

Syntax hints:   -> wi 4   /\ w3a 1037   /\ w-bnj17 30752

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-3an 1039  df-bnj17 30753

This theorem is referenced by:  bnj966  31014  bnj967  31015  bnj910  31018  bnj1006  31029  bnj1118  31052  bnj1177  31074