Theorem eubidv 2087

Description: Formula-building rule for unique existential quantifier (deduction form). (Contributed by NM, 9-Jul-1994.)

Hypothesis

Ref	Expression
eubidv.1	|- ( ph -> ( ps <-> ch ) )

Assertion

Ref	Expression
eubidv	|- ( ph -> ( E! x ps <-> E! x ch ) )

Distinct variable group:   ph, x

Allowed substitution hints:   ps( x)   ch( x)

Proof of Theorem eubidv

Step	Hyp	Ref	Expression
1		nfv 1576	. 2 |- F/ x ph
2		eubidv.1	. 2 |- ( ph -> ( ps <-> ch ) )
3	1, 2	eubid 2086	1 |- ( ph -> ( E! x ps <-> E! x ch ) )

Syntax hints:   -> wi 4   <-> wb 105   E!weu 2079

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-5 1495  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-4 1558  ax-17 1574  ax-ial 1582

This theorem depends on definitions:  df-bi 117  df-nf 1509  df-eu 2082

This theorem is referenced by:  eubii  2088  eueq2dc  2979  eueq3dc  2980  reuhypd  4568  feu  5519  funfveu  5652  dff4im  5793  acexmid  6016  upxp  14995  dedekindicc  15356