Theorem mooran1 2086

Description: "At most one" imports disjunction to conjunction. (The proof was shortened by Andrew Salmon, 9-Jul-2011.)

Assertion

Ref	Expression
mooran1	|- ((E*xph \/ E*xps) -> E*x(ph /\ ps))

Proof of Theorem mooran1

Step	Hyp	Ref	Expression
1		simpl 437	. . 3 |- ((ph /\ ps) -> ph)
2	1	immoi 2079	. 2 |- (E*xph -> E*x(ph /\ ps))
3		moan 2083	. 2 |- (E*xps -> E*x(ph /\ ps))
4	2, 3	jaoi 453	1 |- ((E*xph \/ E*xps) -> E*x(ph /\ ps))

Syntax hints:   -> wi 3   \/ wo 336   /\ wa 337  E*wmo 2038

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 1592  ax-gen 1593  ax-8 1594  ax-9 1595  ax-10 1596  ax-11 1597  ax-12 1598  ax-17 1605  ax-4 1608  ax-5o 1610  ax-6o 1613  ax-9o 1763  ax-10o 1781  ax-16 1854  ax-11o 1864

This theorem depends on definitions:  df-bi 220  df-or 338  df-an 339  df-ex 1616  df-sb 1816  df-eu 2041  df-mo 2042

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