Theorem nineq1i 3238

Description: Equality inference for anti-intersection. (Contributed by SF, 11-Jan-2015.)

Hypothesis

Ref	Expression
nineqi.1	|- A = B

Assertion

Ref	Expression
nineq1i	|- (A &ncap C) = (B &ncap C)

Proof of Theorem nineq1i

Step	Hyp	Ref	Expression
1		nineqi.1	. 2 |- A = B
2		nineq1 3235	. 2 |- (A = B -> (A &ncap C) = (B &ncap C))
3	1, 2	ax-mp 5	1 |- (A &ncap C) = (B &ncap C)

Syntax hints:   = wceq 1642   &ncap cnin 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-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-nin 3212

This theorem is referenced by: (None)