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Metamath Proof Explorer

Theorem e1a

Description: A Virtual deduction elimination rule. syl is e1a without virtual deductions. (Contributed by Alan Sare, 11-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e1a.1 
|- (. ph ->. ps ).
e1a.2 
|- ( ps -> ch )
Assertion e1a 
|- (. ph ->. ch ).

Proof

Step Hyp Ref Expression
1 e1a.1 
 |-  (. ph ->. ps ).
2 e1a.2 
 |-  ( ps -> ch )
3 1 in1 
 |-  ( ph -> ps )
4 3 2 syl 
 |-  ( ph -> ch )
5 4 dfvd1ir 
 |-  (. ph ->. ch ).