Theorem jca31 292

Description: Join three consequents. (Contributed by Jeff Hankins, 1-Aug-2009.)

Hypotheses

Ref	Expression
jca31.1	|- ( ph -> ps )
jca31.2	|- ( ph -> ch )
jca31.3	|- ( ph -> th )

Assertion

Ref	Expression
jca31	|- ( ph -> ( ( ps /\ ch ) /\ th ) )

Proof of Theorem jca31

Step	Hyp	Ref	Expression
1		jca31.1	. . 3 |- ( ph -> ps )
2		jca31.2	. . 3 |- ( ph -> ch )
3	1, 2	jca 290	. 2 |- ( ph -> ( ps /\ ch ) )
4		jca31.3	. 2 |- ( ph -> th )
5	3, 4	jca 290	1 |- ( ph -> ( ( ps /\ ch ) /\ th ) )

Syntax hints:   -> wi 4   /\ wa 97

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 101

This theorem is referenced by:  3jca  1084  syl21anc  1134  f1oiso2  5466  nnnq0lem1  6544  prmuloc  6664  prsrlem1  6827  apreap  7578  lemulge11  7832  elnnz  8255  leexp1a  9309