Theorem 2exim 16331

Description: Theorem *11.34 in [WhiteheadRussell] p. 162. Theorem 19.22 of [Margaris] p. 90 with 2 quantifiers.

Assertion

Ref	Expression
2exim	|- (A.xA.y(ph -> ps) -> (E.xE.yph -> E.xE.yps))

Proof of Theorem 2exim

Step	Hyp	Ref	Expression
1		exim 1386	. . 3 |- (A.y(ph -> ps) -> (E.yph -> E.yps))
2	1	alimi 1338	. 2 |- (A.xA.y(ph -> ps) -> A.x(E.yph -> E.yps))
3		exim 1386	. 2 |- (A.x(E.yph -> E.yps) -> (E.xE.yph -> E.xE.yps))
4	2, 3	syl 12	1 |- (A.xA.y(ph -> ps) -> (E.xE.yph -> E.xE.yps))

Syntax hints:   -> wi 3  A.wal 1296  E.wex 1326

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1305  ax-4 1319  ax-5o 1321

This theorem depends on definitions:  df-bi 164  df-an 242  df-ex 1327

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