Theorem mooran1 1418

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

Assertion

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

Proof of Theorem mooran1

Step	Hyp	Ref	Expression
1		moan 1415	. . 3 |- (E*xph -> E*x(ps /\ ph))
2		ancom 435	. . . 4 |- ((ps /\ ph) <-> (ph /\ ps))
3	2	mobii 1398	. . 3 |- (E*x(ps /\ ph) <-> E*x(ph /\ ps))
4	1, 3	sylib 198	. 2 |- (E*xph -> E*x(ph /\ ps))
5		moan 1415	. 2 |- (E*xps -> E*x(ph /\ ps))
6	4, 5	jaoi 341	1 |- ((E*xph \/ E*xps) -> E*x(ph /\ ps))

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

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