This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem 19.3

Description: A wff may be quantified with a variable not free in it. Version of 19.9 with a universal quantifier. Theorem 19.3 of Margaris p. 89. See 19.3v for a version requiring fewer axioms. (Contributed by NM, 12-Mar-1993) (Revised by Mario Carneiro, 24-Sep-2016)

Ref Expression
Hypothesis 19.3.1 
|- F/ x ph
Assertion 19.3 
|- ( A. x ph <-> ph )

Proof

Step Hyp Ref Expression
1 19.3.1 
 |-  F/ x ph
2 sp 
 |-  ( A. x ph -> ph )
3 1 nf5ri 
 |-  ( ph -> A. x ph )
4 2 3 impbii 
 |-  ( A. x ph <-> ph )