Theorem eubidv 2063

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 1552	. 2 |- F/ x ph
2		eubidv.1	. 2 |- ( ph -> ( ps <-> ch ) )
3	1, 2	eubid 2062	1 |- ( ph -> ( E! x ps <-> E! x ch ) )

Syntax hints:   -> wi 4   <-> wb 105   E!weu 2055

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 1471  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-4 1534  ax-17 1550  ax-ial 1558

This theorem depends on definitions:  df-bi 117  df-nf 1485  df-eu 2058

This theorem is referenced by:  eubii  2064  eueq2dc  2950  eueq3dc  2951  reuhypd  4526  feu  5470  funfveu  5602  dff4im  5739  acexmid  5956  upxp  14819  dedekindicc  15180