Theorem mooran2 1426

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 1424	. 2 |- (E*x(ph \/ ps) -> E*xph)
2		orcom 246	. . . 4 |- ((ph \/ ps) <-> (ps \/ ph))
3	2	mobii 1405	. . 3 |- (E*x(ph \/ ps) <-> E*x(ps \/ ph))
4		moor 1424	. . 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 1381

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-11 967  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 981  df-sb 1172  df-eu 1382  df-mo 1383

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