Theorem moan 2524

Description: "At most one" is still the case when a conjunct is added. (Contributed by NM, 22-Apr-1995.)

Assertion

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

Proof of Theorem moan

Step	Hyp	Ref	Expression
1		simpr 477	. 2 |- ( ( ps /\ ph ) -> ph )
2	1	moimi 2520	1 |- ( E* x ph -> E* x ( ps /\ ph ) )

Syntax hints:   -> wi 4   /\ wa 384   E*wmo 2471

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1705  df-nf 1710  df-eu 2474  df-mo 2475

This theorem is referenced by:  moani  2525  mooran1  2527  moanim  2529  mormo  3158  rmoan  3406