Theorem hbmo1 1406

Description: Bound-variable hypothesis builder for "at most one."

Assertion

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

Proof of Theorem hbmo1

Step	Hyp	Ref	Expression
1		hbe1 1016	. . 3 |- (E.xph -> A.xE.xph)
2		hbeu1 1388	. . 3 |- (E!xph -> A.xE!xph)
3	1, 2	hbim 1007	. 2 |- ((E.xph -> E!xph) -> A.x(E.xph -> E!xph))
4		df-mo 1383	. 2 |- (E*xph <-> (E.xph -> E!xph))
5	4	albii 999	. 2 |- (A.xE*xph <-> A.x(E.xph -> E!xph))
6	3, 4, 5	3imtr4 219	1 |- (E*xph -> A.xE*xph)

Syntax hints:   -> wi 3  A.wal 954  E.wex 980  E!weu 1380  E*wmo 1381

This theorem is referenced by:  moanmo 1431  mopick2 1436  moexex 1438  2eu3 1451

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-4 973  ax-5o 975  ax-6o 978

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-eu 1382  df-mo 1383

Copyright terms: Public domain