Theorem dffun6OLD 6579

Description: Obsolete version of dffun6 6573 as of 19-Dec-2024. (Contributed by NM, 9-Mar-1995.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
dffun6OLD	⊢ (Fun 𝐹 ↔ (Rel 𝐹 ∧ ∀𝑥∃*𝑦 𝑥𝐹𝑦))

Distinct variable group:   𝑥,𝑦,𝐹

Proof of Theorem dffun6OLD

Step	Hyp	Ref	Expression
1		nfcv 2904	. 2 ⊢ Ⅎ𝑥𝐹
2		nfcv 2904	. 2 ⊢ Ⅎ𝑦𝐹
3	1, 2	dffun6f 6578	1 ⊢ (Fun 𝐹 ↔ (Rel 𝐹 ∧ ∀𝑥∃*𝑦 𝑥𝐹𝑦))

Syntax hints:   ↔ wb 206   ∧ wa 395  ∀wal 1537  ∃*wmo 2537   class class class wbr 5142  Rel wrel 5689  Fun wfun 6554

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-10 2140  ax-11 2156  ax-12 2176  ax-ext 2707  ax-sep 5295  ax-nul 5305  ax-pr 5431

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1542  df-fal 1552  df-ex 1779  df-nf 1783  df-sb 2064  df-mo 2539  df-clab 2714  df-cleq 2728  df-clel 2815  df-nfc 2891  df-ral 3061  df-rex 3070  df-rab 3436  df-v 3481  df-dif 3953  df-un 3955  df-ss 3967  df-nul 4333  df-if 4525  df-sn 4626  df-pr 4628  df-op 4632  df-br 5143  df-opab 5205  df-id 5577  df-xp 5690  df-rel 5691  df-cnv 5692  df-co 5693  df-fun 6562

This theorem is referenced by: (None)