Theorem eubidv 1385

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-17 970	. 2 |- (ph -> A.xph)
2		eubidv.1	. 2 |- (ph -> (ps <-> ch))
3	1, 2	eubid 1384	1 |- (ph -> (E!xps <-> E!xch))

Syntax hints:   -> wi 3   <-> wb 146  E!weu 1379

This theorem is referenced by:  reubidva 1777  eueq2 1915  eueq3 1916  moeq3 1918  reuhyp 2901  fneu 3588  feu 3642  tz6.12-2 3734  fnbrfvb 3748  dff2 3812  dff3 3813  aceq5lem5 4722  aceq5 4723  kmlem2 4749  kmlem12 4759  kmlem13 4760  supxrre 6040  pjtheut 9191

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 962  ax-17 970  ax-4 972  ax-5o 974

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 980  df-eu 1381

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