Theorem dffun6OLD 6562

Description: Obsolete version of dffun6 6556 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 2903	. 2 ⊢ Ⅎ𝑥𝐹
2		nfcv 2903	. 2 ⊢ Ⅎ𝑦𝐹
3	1, 2	dffun6f 6561	1 ⊢ (Fun 𝐹 ↔ (Rel 𝐹 ∧ ∀𝑥∃*𝑦 𝑥𝐹𝑦))

Syntax hints:   ↔ wb 205   ∧ wa 396  ∀wal 1539  ∃*wmo 2532   class class class wbr 5148  Rel wrel 5681  Fun wfun 6537

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-10 2137  ax-11 2154  ax-12 2171  ax-ext 2703  ax-sep 5299  ax-nul 5306  ax-pr 5427

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3an 1089  df-tru 1544  df-fal 1554  df-ex 1782  df-nf 1786  df-sb 2068  df-mo 2534  df-clab 2710  df-cleq 2724  df-clel 2810  df-nfc 2885  df-ral 3062  df-rex 3071  df-rab 3433  df-v 3476  df-dif 3951  df-un 3953  df-in 3955  df-ss 3965  df-nul 4323  df-if 4529  df-sn 4629  df-pr 4631  df-op 4635  df-br 5149  df-opab 5211  df-id 5574  df-xp 5682  df-rel 5683  df-cnv 5684  df-co 5685  df-fun 6545

This theorem is referenced by: (None)