Theorem eubidv 1905

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!xps <-> E!xch))

Distinct variable group:   ph,x

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

Proof of Theorem eubidv

Step	Hyp	Ref	Expression
1		nfv 1418	. 2 |- F/xph
2		eubidv.1	. 2 |- (ph -> (ps <-> ch))
3	1, 2	eubid 1904	1 |- (ph -> (E!xps <-> E!xch))

Syntax hints:   -> wi 4   <-> wb 98  E!weu 1897

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 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424

This theorem depends on definitions:  df-bi 110  df-nf 1347  df-eu 1900

This theorem is referenced by:  eubii  1906  eueq2dc  2708  eueq3dc  2709  reuhypd  4169  feu  5015  funfveu  5131  dff4im  5256  acexmid  5454