Theorem negeqi 4137

Description: Equality inference for negatives.

Hypothesis

Ref	Expression
negeqi.1	⊢ A = B

Assertion

Ref	Expression
negeqi	⊢ -A = -B

Proof of Theorem negeqi

Step	Hyp	Ref	Expression
1		negeqi.1	. 2 ⊢ A = B
2		negeq 4136	. 2 ⊢ (A = B → -A = -B)
3	1, 2	ax-mp 6	1 ⊢ -A = -B

Syntax hints:   = wceq 1091  -cneg 4090

This theorem is referenced by:  mulneg2 4191  mul2neg 4192  negdi 4193  negdi2 4194  recgt0i 4385  crmult 4530  discrlem1 4713  sqrlem11 4741  reneg 4824  imneg 4826  cjneg 4827  normlem1 5063  pjthlem5 5229

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-13 804  ax-14 805  ax-16 922  ax-17 925  ax-ext 1074  ax-rep 1075  ax-pow 1077

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-v 1349  df-dif 1489  df-un 1490  df-in 1491  df-ss 1492  df-nul 1708  df-pw 1799  df-sn 1811  df-pr 1812  df-op 1815  df-uni 1920  df-br 2063  df-opab 2098  df-xp 2424  df-cnv 2426  df-dm 2428  df-rn 2429  df-res 2430  df-ima 2431  df-fv 2438  df-opr 3003  df-neg 4135

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