Theorem 19.23vv 1892

Description: Theorem 19.23 of [Margaris] p. 90 extended to two variables. (Contributed by NM, 10-Aug-2004.)

Assertion

Ref	Expression
19.23vv	|- (A.xA.y(ph -> ps) <-> (E.xE.yph -> ps))

Distinct variable groups:   ps,x   ps,y

Allowed substitution hints:   ph(x,y)

Proof of Theorem 19.23vv

Step	Hyp	Ref	Expression
1		19.23v 1891	. . 3 |- (A.y(ph -> ps) <-> (E.yph -> ps))
2	1	albii 1566	. 2 |- (A.xA.y(ph -> ps) <-> A.x(E.yph -> ps))
3		19.23v 1891	. 2 |- (A.x(E.yph -> ps) <-> (E.xE.yph -> ps))
4	2, 3	bitri 240	1 |- (A.xA.y(ph -> ps) <-> (E.xE.yph -> ps))

Syntax hints:   -> wi 4   <-> wb 176  A.wal 1540  E.wex 1541

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545

This theorem is referenced by:  ssrelk  4212  eqrelk  4213  sikexlem  4296  insklem  4305  raliunxp  4824  ssopr  4847