Theorem hbmo1 1935

Description: Bound-variable hypothesis builder for "at most one." (Contributed by NM, 8-Mar-1995.)

Assertion

Ref	Expression
hbmo1	|- (E*xph -> A.xE*xph)

Proof of Theorem hbmo1

Step	Hyp	Ref	Expression
1		df-mo 1901	. 2 |- (E*xph <-> (E.xph -> E!xph))
2		hbe1 1381	. . 3 |- (E.xph -> A.xE.xph)
3		hbeu1 1907	. . 3 |- (E!xph -> A.xE!xph)
4	2, 3	hbim 1434	. 2 |- ((E.xph -> E!xph) -> A.x(E.xph -> E!xph))
5	1, 4	hbxfrbi 1358	1 |- (E*xph -> A.xE*xph)

Syntax hints:   -> wi 4  A.wal 1240  E.wex 1378  E!weu 1897  E*wmo 1898

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-ial 1424  ax-i5r 1425

This theorem depends on definitions:  df-bi 110  df-eu 1900  df-mo 1901

This theorem is referenced by:  mopick2  1980  moexexdc  1981