Theorem eubidv 1363

Description: Formula-building rule for uniqueness quantifier (deduction rule).

Hypothesis

Ref	Expression
eubidv.1	|- (ph -> (ps <-> ch))

Assertion

Ref	Expression
eubidv	|- (ph -> (E!xps <-> E!xch))

Distinct variable group:   ph,x

Proof of Theorem eubidv

Step	Hyp	Ref	Expression
1		ax-17 1190	. 2 |- (ph -> A.xph)
2		eubidv.1	. 2 |- (ph -> (ps <-> ch))
3	1, 2	eubid 1362	1 |- (ph -> (E!xps <-> E!xch))

Syntax hints:   -> wi 3   <-> wb 146  E!weu 1357

This theorem is referenced by:  reubidva 1755  eueq2 1890  eueq3 1891  moeq3 1893  reuhyp 2868  fneu 3532  feu 3586  tz6.12-2 3678  fnbrfvb 3692  dff2 3756  dff3 3757  aceq5lem5 4663  aceq5 4664  kmlem2 4690  kmlem12 4700  kmlem13 4701  supxrre 5981  pjtheut 9365

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-4 951  ax-5 952  ax-gen 955  ax-17 1190

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 957  df-eu 1359

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