Theorem mosub 2862

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 2861	. 2 |- ( A. y E* x ph -> E* x E. y ( y = A /\ ph ) )
2		mosub.1	. 2 |- E* x ph
3	1, 2	mpg 1427	1 |- E* x E. y ( y = A /\ ph )

Syntax hints:   /\ wa 103   = wceq 1331   E.wex 1468   E*wmo 2000

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-eu 2002  df-mo 2003  df-clab 2126  df-cleq 2132  df-clel 2135  df-v 2688

This theorem is referenced by: (None)