Theorem 19.40-2 16334

Description: Theorem *11.42 in [WhiteheadRussell] p. 163. Theorem 19.40 of [Margaris] p. 90 with 2 quantifiers.

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 1447	. . 3 |- (E.y(ph /\ ps) -> (E.yph /\ E.yps))
2	1	eximi 1387	. 2 |- (E.xE.y(ph /\ ps) -> E.x(E.yph /\ E.yps))
3		19.40 1447	. 2 |- (E.x(E.yph /\ E.yps) -> (E.xE.yph /\ E.xE.yps))
4	2, 3	syl 12	1 |- (E.xE.y(ph /\ ps) -> (E.xE.yph /\ E.xE.yps))

Syntax hints:   -> wi 3   /\ wa 240  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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