Theorem 19.3v 1755

Description: Version of 19.3 1888 with a dv condition, requiring fewer axioms. Any formula can be universally quantified using a variable which it does not contain. See also 19.9v 1754. (Contributed by Anthony Hart, 13-Sep-2011.) Remove dependency on ax-7 1790. (Revised by Wolf Lammen, 4-Dec-2017.)

Assertion

Ref	Expression
19.3v

Distinct variable group:   ,

Proof of Theorem 19.3v

Step	Hyp	Ref	Expression
1		alex 1647	. 2
2		19.9v 1754	. . 3
3	2	con2bii 332	. 2
4	1, 3	bitr4i 252	1

Syntax hints:  -.wn 3  <->wb 184  A.wal 1393  E.wex 1612

This theorem is referenced by:  spvw  1756  19.27v  1766  19.28v  1767  19.37v  1768  axrep1  4564  kmlem14  8564  zfcndrep  9013  zfcndpow  9015  zfcndac  9018  dford4  30971  bj-axrep1  34374  bj-snsetex  34521

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747

This theorem depends on definitions:  df-bi 185  df-ex 1613