Theorem mooran2 1419

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 1417	. 2 |- (E*x(ph \/ ps) -> E*xph)
2		orcom 246	. . . 4 |- ((ph \/ ps) <-> (ps \/ ph))
3	2	mobii 1398	. . 3 |- (E*x(ph \/ ps) <-> E*x(ps \/ ph))
4		moor 1417	. . 3 |- (E*x(ps \/ ph) -> E*xps)
5	3, 4	sylbi 199	. 2 |- (E*x(ph \/ ps) -> E*xps)
6	1, 5	jca 288	1 |- (E*x(ph \/ ps) -> (E*xph /\ E*xps))

Syntax hints:   -> wi 3   \/ wo 222   /\ wa 223  E*wmo 1374

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-10 963  ax-11 964  ax-12 965  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-10o 1136  ax-16 1206  ax-11o 1213

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 978  df-sb 1168  df-eu 1375  df-mo 1376

Copyright terms: Public domain