Metamath Proof Explorer


Theorem e2bir

Description: Right biconditional form of e2 . syl6ibr is e2bir without virtual deductions. (Contributed by Alan Sare, 29-Apr-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e2bir.1
|- (. ph ,. ps ->. ch ).
e2bir.2
|- ( th <-> ch )
Assertion e2bir
|- (. ph ,. ps ->. th ).

Proof

Step Hyp Ref Expression
1 e2bir.1
 |-  (. ph ,. ps ->. ch ).
2 e2bir.2
 |-  ( th <-> ch )
3 2 biimpri
 |-  ( ch -> th )
4 1 3 e2
 |-  (. ph ,. ps ->. th ).