Theorem 19.29x 1070

Description: Variation of Theorem 19.29 of [Margaris] p. 90 with mixed quantification.

Assertion

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

Proof of Theorem 19.29x

Step	Hyp	Ref	Expression
1		19.29r 1068	. 2 |- ((E.xA.yph /\ A.xE.yps) -> E.x(A.yph /\ E.yps))
2		19.29 1067	. . 3 |- ((A.yph /\ E.yps) -> E.y(ph /\ ps))
3	2	19.22i 1036	. 2 |- (E.x(A.yph /\ E.yps) -> E.xE.y(ph /\ ps))
4	1, 3	syl 10	1 |- ((E.xA.yph /\ A.xE.yps) -> E.xE.y(ph /\ ps))

Syntax hints:   -> wi 3   /\ wa 223  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-4 970  ax-5o 972

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

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