Theorem 19.29r2 1073

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

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 1072	. 2 |- ((E.xE.yph /\ A.xA.yps) -> E.x(E.yph /\ A.yps))
2		19.29r 1072	. . 3 |- ((E.yph /\ A.yps) -> E.y(ph /\ ps))
3	2	19.22i 1040	. 2 |- (E.x(E.yph /\ A.yps) -> E.xE.y(ph /\ ps))
4	1, 3	syl 10	1 |- ((E.xE.yph /\ A.xA.yps) -> E.xE.y(ph /\ ps))

Syntax hints:   -> wi 3   /\ wa 223  A.wal 954  E.wex 980

This theorem is referenced by:  2eu6 1454

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-4 973  ax-5o 975

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981

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