Theorem nfneg 8152

Description: Bound-variable hypothesis builder for the negative of a complex number. (Contributed by NM, 12-Jun-2005.) (Revised by Mario Carneiro, 15-Oct-2016.)

Hypothesis

Ref	Expression
nfneg.1	⊢ Ⅎ𝑥𝐴

Assertion

Ref	Expression
nfneg	⊢ Ⅎ𝑥-𝐴

Proof of Theorem nfneg

Step	Hyp	Ref	Expression
1		nfneg.1	. . . 4 ⊢ Ⅎ𝑥𝐴
2	1	a1i 9	. . 3 ⊢ (⊤ → Ⅎ𝑥𝐴)
3	2	nfnegd 8151	. 2 ⊢ (⊤ → Ⅎ𝑥-𝐴)
4	3	mptru 1362	1 ⊢ Ⅎ𝑥-𝐴

Syntax hints:  ⊤wtru 1354  Ⅎwnfc 2306  -cneg 8127

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-rex 2461  df-v 2739  df-un 3133  df-sn 3598  df-pr 3599  df-op 3601  df-uni 3810  df-br 4004  df-iota 5178  df-fv 5224  df-ov 5877  df-neg 8129

This theorem is referenced by:  infssuzcldc  11946