Theorem jca31 302

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 300	. 2 |- ( ph -> ( ps /\ ch ) )
4		jca31.3	. 2 |- ( ph -> th )
5	3, 4	jca 300	1 |- ( ph -> ( ( ps /\ ch ) /\ th ) )

Syntax hints:   -> wi 4   /\ wa 102

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 106

This theorem is referenced by:  3jca  1118  syl21anc  1168  f1oiso2  5486  nnnq0lem1  6636  prmuloc  6756  prsrlem1  6919  apreap  7687  lemulge11  7944  elnnz  8361  supinfneg  8683  infsupneg  8684  leexp1a  9531  faclbnd6  9671  oddpwdclemdc  10551