Theorem mooran2 1465

Description: "At most one" exports disjunction to conjunction.

Assertion

Ref	Expression
mooran2	|- (E*x(ph \/ ps) -> (E*xph /\ E*xps))

Proof of Theorem mooran2

Step	Hyp	Ref	Expression
1		moor 1463	. 2 |- (E*x(ph \/ ps) -> E*xph)
2		orcom 244	. . . 4 |- ((ph \/ ps) <-> (ps \/ ph))
3	2	mobii 1444	. . 3 |- (E*x(ph \/ ps) <-> E*x(ps \/ ph))
4		moor 1463	. . 3 |- (E*x(ps \/ ph) -> E*xps)
5	3, 4	sylbi 197	. 2 |- (E*x(ph \/ ps) -> E*xps)
6	1, 5	jca 286	1 |- (E*x(ph \/ ps) -> (E*xph /\ E*xps))

Syntax hints:   -> wi 3   \/ wo 220   /\ wa 221  E*wmo 1420

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 998  ax-gen 999  ax-8 1000  ax-10 1002  ax-11 1003  ax-12 1004  ax-17 1007  ax-4 1009  ax-5o 1011  ax-6o 1014  ax-9o 1159  ax-10o 1177  ax-16 1247  ax-11o 1255

This theorem depends on definitions:  df-bi 145  df-or 222  df-an 223  df-ex 1017  df-sb 1209  df-eu 1421  df-mo 1422

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