Theorem inf1 8060

Description: Variation of Axiom of Infinity (using zfinf 8077 as a hypothesis). Axiom of Infinity in [FreydScedrov] p. 283. (Contributed by NM, 14-Oct-1996.) (Revised by David Abernethy, 1-Oct-2013.)

Hypothesis

Ref	Expression
inf1.1

Assertion

Ref	Expression
inf1

Proof of Theorem inf1

Step	Hyp	Ref	Expression
1		inf1.1	. 2
2		ne0i 3790	. . 3
3	2	anim1i 568	. 2
4	1, 3	eximii 1658	1

Syntax hints:  ->wi 4  /\wa 369  A.wal 1393  E.wex 1612  =/=wne 2652  c0 3784

This theorem is referenced by:  inf2  8061

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-ne 2654  df-v 3111  df-dif 3478  df-nul 3785