Theorem eubidv 2085

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 1574	. 2 |- F/ x ph
2		eubidv.1	. 2 |- ( ph -> ( ps <-> ch ) )
3	1, 2	eubid 2084	1 |- ( ph -> ( E! x ps <-> E! x ch ) )

Syntax hints:   -> wi 4   <-> wb 105   E!weu 2077

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 1493  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-4 1556  ax-17 1572  ax-ial 1580

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-eu 2080

This theorem is referenced by:  eubii  2086  eueq2dc  2976  eueq3dc  2977  reuhypd  4561  feu  5507  funfveu  5639  dff4im  5780  acexmid  5999  upxp  14940  dedekindicc  15301