Theorem eubidv 1386

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-17 971	. 2 |- (ph -> A.xph)
2		eubidv.1	. 2 |- (ph -> (ps <-> ch))
3	1, 2	eubid 1385	1 |- (ph -> (E!xps <-> E!xch))

Syntax hints:   -> wi 3   <-> wb 146  E!weu 1380

This theorem is referenced by:  reubidva 1779  eueq2 1918  eueq3 1919  moeq3 1921  reuhyp 2905  fneu 3592  feu 3647  tz6.12-2 3739  fnbrfvb 3753  dff2 3817  dff3 3818  aceq5lem5 4739  aceq5 4740  kmlem2 4766  kmlem12 4776  kmlem13 4777  supxrre 6083  pjtheut 9236

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-17 971  ax-4 973  ax-5o 975

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-eu 1382

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