Metamath Proof Explorer


Theorem 3jaao

Description: Inference conjoining and disjoining the antecedents of three implications. (Contributed by Jeff Hankins, 15-Aug-2009) (Proof shortened by Andrew Salmon, 13-May-2011)

Ref Expression
Hypotheses 3jaao.1 φψχ
3jaao.2 θτχ
3jaao.3 ηζχ
Assertion 3jaao φθηψτζχ

Proof

Step Hyp Ref Expression
1 3jaao.1 φψχ
2 3jaao.2 θτχ
3 3jaao.3 ηζχ
4 1 3ad2ant1 φθηψχ
5 2 3ad2ant2 φθητχ
6 3 3ad2ant3 φθηζχ
7 4 5 6 3jaod φθηψτζχ