Theorem nceqi 6110

Description: Equality inference for cardinality. (Contributed by SF, 24-Feb-2015.)

Hypothesis

Ref	Expression
nceqi.1	⊢ A = B

Assertion

Ref	Expression
nceqi	⊢ Nc A = Nc B

Proof of Theorem nceqi

Step	Hyp	Ref	Expression
1		nceqi.1	. 2 ⊢ A = B
2		nceq 6109	. 2 ⊢ (A = B → Nc A = Nc B)
3	1, 2	ax-mp 5	1 ⊢ Nc A = Nc B

Syntax hints:   = wceq 1642   Nc cnc 6092

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-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2479  df-rex 2621  df-sn 3742  df-ima 4728  df-ec 5948  df-nc 6102

This theorem is referenced by:  muc0  6143  ncpw1c  6155  1p1e2c  6156  2p1e3c  6157  ce0  6191  ce2nc1  6194  tcncv  6227  addcdi  6251  nchoicelem19  6308  vncan  6338