Metamath Proof Explorer


Theorem orim12d

Description: Disjoin antecedents and consequents in a deduction. See orim12dALT for a proof which does not depend on df-an . (Contributed by NM, 10-May-1994)

Ref Expression
Hypotheses orim12d.1 φ ψ χ
orim12d.2 φ θ τ
Assertion orim12d φ ψ θ χ τ

Proof

Step Hyp Ref Expression
1 orim12d.1 φ ψ χ
2 orim12d.2 φ θ τ
3 pm3.48 ψ χ θ τ ψ θ χ τ
4 1 2 3 syl2anc φ ψ θ χ τ