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Metamath Proof Explorer

Theorem el1

Description: A Virtual deduction elimination rule. syl is el1 without virtual deductions. (Contributed by Alan Sare, 23-Apr-2015) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses el1.1 
|- (. ph ->. ps ).
el1.2 
|- ( ps -> ch )
Assertion el1 
|- (. ph ->. ch ).

Proof

Step Hyp Ref Expression
1 el1.1 
 |-  (. ph ->. ps ).
2 el1.2 
 |-  ( ps -> ch )
3 1 in1 
 |-  ( ph -> ps )
4 3 2 syl 
 |-  ( ph -> ch )
5 4 dfvd1ir 
 |-  (. ph ->. ch ).