Theorem r19.40 1754

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		pm3.26 319	. . 3 |- ((ph /\ ps) -> ph)
2	1	r19.22si 1726	. 2 |- (E.x e. A (ph /\ ps) -> E.x e. A ph)
3		pm3.27 323	. . 3 |- ((ph /\ ps) -> ps)
4	3	r19.22si 1726	. 2 |- (E.x e. A (ph /\ ps) -> E.x e. A ps)
5	2, 4	jca 288	1 |- (E.x e. A (ph /\ ps) -> (E.x e. A ph /\ E.x e. A ps))

Syntax hints:   -> wi 3   /\ wa 223  E.wrex 1638

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 960  ax-4 970  ax-5o 972

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 978  df-ral 1641  df-rex 1642

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