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 ).