Metamath Proof Explorer


Theorem jca31

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

Ref Expression
Hypotheses jca31.1 φψ
jca31.2 φχ
jca31.3 φθ
Assertion jca31 φψχθ

Proof

Step Hyp Ref Expression
1 jca31.1 φψ
2 jca31.2 φχ
3 jca31.3 φθ
4 1 2 jca φψχ
5 4 3 jca φψχθ