Theorem mooran1 1972

Description: "At most one" imports disjunction to conjunction. (Contributed by NM, 5-Apr-2004.) (Proof shortened by Andrew Salmon, 9-Jul-2011.)

Assertion

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

Proof of Theorem mooran1

Step	Hyp	Ref	Expression
1		simpl 102	. . 3 |- ( ( ph /\ ps ) -> ph )
2	1	moimi 1965	. 2 |- ( E* x ph -> E* x ( ph /\ ps ) )
3		moan 1969	. 2 |- ( E* x ps -> E* x ( ph /\ ps ) )
4	2, 3	jaoi 636	1 |- ( ( E* x ph \/ E* x ps ) -> E* x ( ph /\ ps ) )

Syntax hints:   -> wi 4   /\ wa 97   \/ wo 629   E*wmo 1901

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428

This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904

This theorem is referenced by: (None)