Theorem nfneg 7952

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 7951	. 2 ⊢ (⊤ → Ⅎ𝑥-𝐴)
4	3	mptru 1340	1 ⊢ Ⅎ𝑥-𝐴

Syntax hints:  ⊤wtru 1332  Ⅎwnfc 2266  -cneg 7927

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119

This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-rex 2420  df-v 2683  df-un 3070  df-sn 3528  df-pr 3529  df-op 3531  df-uni 3732  df-br 3925  df-iota 5083  df-fv 5126  df-ov 5770  df-neg 7929

This theorem is referenced by:  infssuzcldc  11633