Theorem difeq1i 3382

Description: Inference adding difference to the right in a class equality. (Contributed by NM, 15-Nov-2002.)

Hypothesis

Ref	Expression
difeq1i.1	⊢ A = B

Assertion

Ref	Expression
difeq1i	⊢ (A ∖ C) = (B ∖ C)

Proof of Theorem difeq1i

Step	Hyp	Ref	Expression
1		difeq1i.1	. 2 ⊢ A = B
2		difeq1 3247	. 2 ⊢ (A = B → (A ∖ C) = (B ∖ C))
3	1, 2	ax-mp 5	1 ⊢ (A ∖ C) = (B ∖ C)

Syntax hints:   = wceq 1642   ∖ cdif 3207

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 2479  df-v 2862  df-nin 3212  df-compl 3213  df-in 3214  df-dif 3216

This theorem is referenced by:  difeq12i  3384  dfin3  3495  indif1  3500  indifcom  3501  difun1  3515  notab  3526  notrab  3533  undifabs  3628  difprsn1  3848  difprsn2  3849