Theorem 19.40-2 1610

Description: Theorem *11.42 in [WhiteheadRussell] p. 163. Theorem 19.40 of [Margaris] p. 90 with 2 quantifiers. (Contributed by Andrew Salmon, 24-May-2011.)

Assertion

Ref	Expression
19.40-2	|- (E.xE.y(ph /\ ps) -> (E.xE.yph /\ E.xE.yps))

Proof of Theorem 19.40-2

Step	Hyp	Ref	Expression
1		19.40 1609	. . 3 |- (E.y(ph /\ ps) -> (E.yph /\ E.yps))
2	1	eximi 1576	. 2 |- (E.xE.y(ph /\ ps) -> E.x(E.yph /\ E.yps))
3		19.40 1609	. 2 |- (E.x(E.yph /\ E.yps) -> (E.xE.yph /\ E.xE.yps))
4	2, 3	syl 15	1 |- (E.xE.y(ph /\ ps) -> (E.xE.yph /\ E.xE.yps))

This proof depends on syntax axioms:   -> wi 4   /\ wa 358  E.wex 1541

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557

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

This theorem is used by: (None)