Metamath Proof Explorer

Theorem jaodan

Description: Deduction disjoining the antecedents of two implications. (Contributed by NM, 14-Oct-2005)

Ref Expression
Hypotheses jaodan.1 φ ψ χ
jaodan.2 φ θ χ
Assertion jaodan φ ψ θ χ


Step Hyp Ref Expression
1 jaodan.1 φ ψ χ
2 jaodan.2 φ θ χ
3 1 ex φ ψ χ
4 2 ex φ θ χ
5 3 4 jaod φ ψ θ χ
6 5 imp φ ψ θ χ