Theorem moani 1416

Description: "At most one" is still true when a conjunct is added.

Hypothesis

Ref	Expression
moani.1	|- E*xph

Assertion

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

Proof of Theorem moani

Step	Hyp	Ref	Expression
1		moani.1	. 2 |- E*xph
2		moan 1415	. 2 |- (E*xph -> E*x(ps /\ ph))
3	1, 2	ax-mp 7	1 |- E*x(ps /\ ph)

Syntax hints:   /\ wa 223  E*wmo 1374

This theorem is referenced by:  euxfr2 1916  reuxfr2 2893  opabex2g 3597  fconst 3643  oprabex2g 4005  2ndconst 4081  axaddopr 5237  axmulopr 5238

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

Copyright terms: Public domain