Theorem moani 1422

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 1421	. 2 |- (E*xph -> E*x(ps /\ ph))
3	1, 2	ax-mp 7	1 |- E*x(ps /\ ph)

Syntax hints:   /\ wa 223  E*wmo 1380

This theorem is referenced by:  euxfr2 1923  reuxfr2 2899  opabex2g 3607  fconst 3653  oprabex2g 4015  2ndconst 4090  axaddopr 5248  axmulopr 5249

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 961  ax-gen 962  ax-8 963  ax-10 965  ax-11 966  ax-12 967  ax-17 970  ax-4 972  ax-5o 974  ax-6o 977  ax-9o 1122  ax-10o 1139  ax-16 1209  ax-11o 1217

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 980  df-sb 1171  df-eu 1381  df-mo 1382

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