Theorem 19.23vv 1289

Description: Theorem 19.23 of [Margaris] p. 90 extended to two variables.

Assertion

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

Distinct variable groups:   ps,x   ps,y

Proof of Theorem 19.23vv

Step	Hyp	Ref	Expression
1		19.23v 1288	. . 3 |- (A.y(ph -> ps) <-> (E.yph -> ps))
2	1	albii 996	. 2 |- (A.xA.y(ph -> ps) <-> A.x(E.yph -> ps))
3		19.23v 1288	. 2 |- (A.x(E.yph -> ps) <-> (E.xE.yph -> ps))
4	2, 3	bitr 173	1 |- (A.xA.y(ph -> ps) <-> (E.xE.yph -> ps))

Syntax hints:   -> wi 3   <-> wb 146  A.wal 951  E.wex 977

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 960  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 978

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