Theorem dffun6OLD 6572

Description: Obsolete version of dffun6 6566 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 2899	. 2 ⊢ Ⅎ𝑥𝐹
2		nfcv 2899	. 2 ⊢ Ⅎ𝑦𝐹
3	1, 2	dffun6f 6571	1 ⊢ (Fun 𝐹 ↔ (Rel 𝐹 ∧ ∀𝑥∃*𝑦 𝑥𝐹𝑦))

Syntax hints:   ↔ wb 205   ∧ wa 394  ∀wal 1531  ∃*wmo 2527   class class class wbr 5152  Rel wrel 5687  Fun wfun 6547

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-10 2129  ax-11 2146  ax-12 2166  ax-ext 2699  ax-sep 5303  ax-nul 5310  ax-pr 5433

This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-nf 1778  df-sb 2060  df-mo 2529  df-clab 2706  df-cleq 2720  df-clel 2806  df-nfc 2881  df-ral 3059  df-rex 3068  df-rab 3431  df-v 3475  df-dif 3952  df-un 3954  df-in 3956  df-ss 3966  df-nul 4327  df-if 4533  df-sn 4633  df-pr 4635  df-op 4639  df-br 5153  df-opab 5215  df-id 5580  df-xp 5688  df-rel 5689  df-cnv 5690  df-co 5691  df-fun 6555

This theorem is referenced by: (None)