Theorem mosub 2938

Description: "At most one" remains true after substitution. (Contributed by NM, 9-Mar-1995.)

Hypothesis

Ref	Expression
mosub.1	|- E* x ph

Assertion

Ref	Expression
mosub	|- E* x E. y ( y = A /\ ph )

Distinct variable group:   x, y, A

Allowed substitution hints:   ph( x, y)

Proof of Theorem mosub

Step	Hyp	Ref	Expression
1		mosubt 2937	. 2 |- ( A. y E* x ph -> E* x E. y ( y = A /\ ph ) )
2		mosub.1	. 2 |- E* x ph
3	1, 2	mpg 1462	1 |- E* x E. y ( y = A /\ ph )

Syntax hints:   /\ wa 104   = wceq 1364   E.wex 1503   E*wmo 2043

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-eu 2045  df-mo 2046  df-clab 2180  df-cleq 2186  df-clel 2189  df-v 2762

This theorem is referenced by: (None)