Theorem r19.40 1301

Description: Restricted quantifier version of Theorem 19.40 of [Margaris] p. 90.

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		pm3.26 256	. . 3 |- ((ph /\ ps) -> ph)
2	1	r19.22si 1275	. 2 |- (E.x e. A (ph /\ ps) -> E.x e. A ph)
3		pm3.27 260	. . 3 |- ((ph /\ ps) -> ps)
4	3	r19.22si 1275	. 2 |- (E.x e. A (ph /\ ps) -> E.x e. A ps)
5	2, 4	jca 236	1 |- (E.x e. A (ph /\ ps) -> (E.x e. A ph /\ E.x e. A ps))

Syntax hints:   -> wi 2   /\ wa 196  E.wrex 1202

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-gen 677

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679  df-ral 1205  df-rex 1206

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