Theorem r19.40 2763

Description: Restricted quantifier version of Theorem 19.40 of [Margaris] p. 90. (Contributed by NM, 2-Apr-2004.)

Assertion

Ref	Expression
r19.40	|- (E.x e. A (ph /\ ps) -> (E.x e. A ph /\ E.x e. A ps))

Proof of Theorem r19.40

Step	Hyp	Ref	Expression
1		simpl 443	. . 3 |- ((ph /\ ps) -> ph)
2	1	reximi 2722	. 2 |- (E.x e. A (ph /\ ps) -> E.x e. A ph)
3		simpr 447	. . 3 |- ((ph /\ ps) -> ps)
4	3	reximi 2722	. 2 |- (E.x e. A (ph /\ ps) -> E.x e. A ps)
5	2, 4	jca 518	1 |- (E.x e. A (ph /\ ps) -> (E.x e. A ph /\ E.x e. A ps))

Syntax hints:   -> wi 4   /\ wa 358  E.wrex 2616

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  df-ral 2620  df-rex 2621

This theorem is referenced by: (None)