Theorem issetf 3114

Description: A version of isset 3113 that does not require and to be distinct. (Contributed by Andrew Salmon, 6-Jun-2011.) (Revised by Mario Carneiro, 10-Oct-2016.)

Hypothesis

Ref	Expression
issetf.1

Assertion

Ref	Expression
issetf

Proof of Theorem issetf

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		isset 3113	. 2
2		issetf.1	. . . 4
3	2	nfeq2 2636	. . 3
4		nfv 1707	. . 3
5		eqeq1 2461	. . 3
6	3, 4, 5	cbvex 2022	. 2
7	1, 6	bitri 249	1

Syntax hints:  <->wb 184  =wceq 1395  E.wex 1612  e.wcel 1818  F/_wnfc 2605  cvv 3109

This theorem is referenced by:  vtoclgf  3165  spcimgft  3185

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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111