Metamath Proof Explorer


Theorem mpbi2and

Description: Detach a conjunction of truths in a biconditional. (Contributed by NM, 6-Nov-2011) (Proof shortened by Wolf Lammen, 24-Nov-2012)

Ref Expression
Hypotheses mpbi2and.1 φ ψ
mpbi2and.2 φ χ
mpbi2and.3 φ ψ χ θ
Assertion mpbi2and φ θ

Proof

Step Hyp Ref Expression
1 mpbi2and.1 φ ψ
2 mpbi2and.2 φ χ
3 mpbi2and.3 φ ψ χ θ
4 1 2 jca φ ψ χ
5 4 3 mpbid φ θ