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Metamath Proof Explorer

Theorem gen11nv

Description: Virtual deduction generalizing rule for one quantifying variable and one virtual hypothesis without distinct variables. alrimih is gen11nv without virtual deductions. (Contributed by Alan Sare, 12-Dec-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses gen11nv.1 
|- ( ph -> A. x ph )
gen11nv.2 
|- (. ph ->. ps ).
Assertion gen11nv 
|- (. ph ->. A. x ps ).

Proof

Step Hyp Ref Expression
1 gen11nv.1 
 |-  ( ph -> A. x ph )
2 gen11nv.2 
 |-  (. ph ->. ps ).
3 2 in1 
 |-  ( ph -> ps )
4 1 3 alrimih 
 |-  ( ph -> A. x ps )
5 4 dfvd1ir 
 |-  (. ph ->. A. x ps ).