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Metamath Proof Explorer

Theorem e2bi

Description: Biconditional form of e2 . imbitrdi is e2bi without virtual deductions. (Contributed by Alan Sare, 10-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e2bi.1 
|- (. ph ,. ps ->. ch ).
e2bi.2 
|- ( ch <-> th )
Assertion e2bi 
|- (. ph ,. ps ->. th ).

Proof

Step Hyp Ref Expression
1 e2bi.1 
 |-  (. ph ,. ps ->. ch ).
2 e2bi.2 
 |-  ( ch <-> th )
3 2 biimpi 
 |-  ( ch -> th )
4 1 3 e2 
 |-  (. ph ,. ps ->. th ).