Theorem reubida 3040

Description: Formula-building rule for restricted existential quantifier (deduction rule). (Contributed by Mario Carneiro, 19-Nov-2016.)

Hypotheses

Ref	Expression
reubida.1
reubida.2

Assertion

Ref	Expression
reubida

Proof of Theorem reubida

Step	Hyp	Ref	Expression
1		reubida.1	. . 3
2		reubida.2	. . . 4
3	2	pm5.32da 641	. . 3
4	1, 3	eubid 2302	. 2
5		df-reu 2814	. 2
6		df-reu 2814	. 2
7	4, 5, 6	3bitr4g 288	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  F/wnf 1616  e.wcel 1818  E!weu 2282  E!wreu 2809

This theorem is referenced by:  reubidva  3041  reuan  32185

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-12 1854

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-eu 2286  df-reu 2814