Metamath Proof Explorer


Theorem e0bir

Description: Elimination rule identical to mpbir . The non-virtual deduction form is the virtual deduction form, which is mpbir . (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e0bir.1 ⊢ φ
e0bir.2 ⊢ ψ ↔ φ
Assertion e0bir ⊢ ψ

Proof

Step Hyp Ref Expression
1 e0bir.1 ⊢ φ
2 e0bir.2 ⊢ ψ ↔ φ
3 1 2 mpbir ⊢ ψ