Theorem 19.29r2 1598

Description: Variation of Theorem 19.29 of [Margaris] p. 90 with double quantification. (Contributed by NM, 3-Feb-2005.)

Assertion

Ref	Expression
19.29r2	|- ((E.xE.yph /\ A.xA.yps) -> E.xE.y(ph /\ ps))

Proof of Theorem 19.29r2

Step	Hyp	Ref	Expression
1		19.29r 1597	. 2 |- ((E.xE.yph /\ A.xA.yps) -> E.x(E.yph /\ A.yps))
2		19.29r 1597	. . 3 |- ((E.yph /\ A.yps) -> E.y(ph /\ ps))
3	2	eximi 1576	. 2 |- (E.x(E.yph /\ A.yps) -> E.xE.y(ph /\ ps))
4	1, 3	syl 15	1 |- ((E.xE.yph /\ A.xA.yps) -> E.xE.y(ph /\ ps))

Syntax hints:   -> wi 4   /\ wa 358  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

This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542

This theorem is referenced by:  2eu6  2289