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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 
|- ph
e0bir.2 
|- ( ps <-> ph )
Assertion e0bir 
|- ps

Proof

Step Hyp Ref Expression
1 e0bir.1 
 |-  ph
2 e0bir.2 
 |-  ( ps <-> ph )
3 1 2 mpbir 
 |-  ps