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Metamath Proof Explorer

Theorem 19.36i

Description: Inference associated with 19.36 . See 19.36iv for a version requiring fewer axioms. (Contributed by NM, 24-Jun-1993)

Ref Expression
Hypotheses 19.36.1 
|- F/ x ps
19.36i.2 
|- E. x ( ph -> ps )
Assertion 19.36i 
|- ( A. x ph -> ps )

Proof

Step Hyp Ref Expression
1 19.36.1 
 |-  F/ x ps
2 19.36i.2 
 |-  E. x ( ph -> ps )
3 1 19.36 
 |-  ( E. x ( ph -> ps ) <-> ( A. x ph -> ps ) )
4 2 3 mpbi 
 |-  ( A. x ph -> ps )