Theorem bnj95 30934

Description: Technical lemma for bnj124 30941. This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Hypothesis

Ref	Expression
bnj95.1	|- F = { <. (/) , pred ( x , A , R ) >. }

Assertion

Ref	Expression
bnj95	|- F e. _V

Proof of Theorem bnj95

Step	Hyp	Ref	Expression
1		bnj95.1	. 2 |- F = { <. (/) , pred ( x , A , R ) >. }
2		snex 4908	. 2 |- { <. (/) , pred ( x , A , R ) >. } e. _V
3	1, 2	eqeltri 2697	1 |- F e. _V

Syntax hints:   = wceq 1483   e. wcel 1990   _Vcvv 3200   (/)c0 3915   {csn 4177   <.cop 4183   predc-bnj14 30754

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602  ax-sep 4781  ax-nul 4789  ax-pr 4906

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-v 3202  df-dif 3577  df-un 3579  df-nul 3916  df-sn 4178  df-pr 4180

This theorem is referenced by:  bnj124  30941  bnj125  30942  bnj126  30943  bnj150  30946