Theorem 19.3h 1553

Description: A wff may be quantified with a variable not free in it. Theorem 19.3 of [Margaris] p. 89. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 21-May-2007.)

Hypothesis

Ref	Expression
19.3h.1	|- ( ph -> A. x ph )

Assertion

Ref	Expression
19.3h	|- ( A. x ph <-> ph )

Proof of Theorem 19.3h

Step	Hyp	Ref	Expression
1		ax-4 1510	. 2 |- ( A. x ph -> ph )
2		19.3h.1	. 2 |- ( ph -> A. x ph )
3	1, 2	impbii 126	1 |- ( A. x ph <-> ph )

Syntax hints:   -> wi 4   <-> wb 105   A.wal 1351

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 107  ax-ia3 108  ax-4 1510

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  19.27h  1560  19.28h  1562  equsalh  1726  2eu4  2119