Theorem nfcompl 3229

Description: Hypothesis builder for complement. (Contributed by SF, 2-Jan-2018.)

Hypothesis

Ref	Expression
nfbool.1	⊢ ℲxA

Assertion

Ref	Expression
nfcompl	⊢ Ⅎx ∼ A

Proof of Theorem nfcompl

Step	Hyp	Ref	Expression
1		df-compl 3212	. 2 ⊢ ∼ A = (A ⩃ A)
2		nfbool.1	. . 3 ⊢ ℲxA
3	2, 2	nfnin 3228	. 2 ⊢ Ⅎx(A ⩃ A)
4	1, 3	nfcxfr 2486	1 ⊢ Ⅎx ∼ A

Syntax hints:  Ⅎwnfc 2476   ⩃ cnin 3204   ∼ ccompl 3205

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-nin 3211  df-compl 3212

This theorem is referenced by:  nfin  3230  nfun  3231  nfdif  3232