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 φ ψ χ
3jaao.2 θ τ χ
3jaao.3 η ζ χ
Assertion 3jaao φ θ η ψ τ ζ χ


Step Hyp Ref Expression
1 3jaao.1 φ ψ χ
2 3jaao.2 θ τ χ
3 3jaao.3 η ζ χ
4 1 3ad2ant1 φ θ η ψ χ
5 2 3ad2ant2 φ θ η τ χ
6 3 3ad2ant3 φ θ η ζ χ
7 4 5 6 3jaod φ θ η ψ τ ζ χ