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Metamath Proof Explorer

Theorem e1bir

Description: Right biconditional form of e1a . sylibr is e1bir without virtual deductions. (Contributed by Alan Sare, 24-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e1bir.1 
|- (. ph ->. ps ).
e1bir.2 
|- ( ch <-> ps )
Assertion e1bir 
|- (. ph ->. ch ).

Proof

Step Hyp Ref Expression
1 e1bir.1 
 |-  (. ph ->. ps ).
2 e1bir.2 
 |-  ( ch <-> ps )
3 2 biimpri 
 |-  ( ps -> ch )
4 1 3 e1a 
 |-  (. ph ->. ch ).