Theorem eubidv 2088

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 1577	. 2 |- F/ x ph
2		eubidv.1	. 2 |- ( ph -> ( ps <-> ch ) )
3	1, 2	eubid 2087	1 |- ( ph -> ( E! x ps <-> E! x ch ) )

Syntax hints:   -> wi 4   <-> wb 105   E!weu 2080

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 1496  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-4 1559  ax-17 1575  ax-ial 1583

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-eu 2083

This theorem is referenced by:  eubii  2089  eueq2dc  2990  eueq3dc  2991  reuhypd  4592  feu  5549  funfveu  5683  dff4im  5823  acexmid  6049  upxp  15137  dedekindicc  15498