Theorem eubidv 1908

Description: Formula-building rule for uniqueness quantifier (deduction rule). (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 1421	. 2 |- F/ x ph
2		eubidv.1	. 2 |- ( ph -> ( ps <-> ch ) )
3	1, 2	eubid 1907	1 |- ( ph -> ( E! x ps <-> E! x ch ) )

Syntax hints:   -> wi 4   <-> wb 98   E!weu 1900

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 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427

This theorem depends on definitions:  df-bi 110  df-nf 1350  df-eu 1903

This theorem is referenced by:  eubii  1909  eueq2dc  2714  eueq3dc  2715  reuhypd  4203  feu  5072  funfveu  5188  dff4im  5313  acexmid  5511