Theorem rmobida 3045

Description: Formula-building rule for restricted existential quantifier (deduction rule). (Contributed by NM, 16-Jun-2017.)

Hypotheses

Ref	Expression
rmobida.1
rmobida.2

Assertion

Ref	Expression
rmobida

Proof of Theorem rmobida

Step	Hyp	Ref	Expression
1		rmobida.1	. . 3
2		rmobida.2	. . . 4
3	2	pm5.32da 641	. . 3
4	1, 3	mobid 2303	. 2
5		df-rmo 2815	. 2
6		df-rmo 2815	. 2
7	4, 5, 6	3bitr4g 288	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  F/wnf 1616  e.wcel 1818  E*wmo 2283  E*wrmo 2810

This theorem is referenced by:  rmobidva  3046  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-mo 2287  df-rmo 2815