Theorem prssi 3864

Description: A pair of elements of a class is a subset of the class. (Contributed by NM, 16-Jan-2015.)

Assertion

Ref	Expression
prssi	|- ((A e. C /\ B e. C) -> {A, B} C_ C)

Proof of Theorem prssi

Step	Hyp	Ref	Expression
1		prssg 3863	. 2 |- ((A e. C /\ B e. C) -> ((A e. C /\ B e. C) <-> {A, B} C_ C))
2	1	ibi 232	1 |- ((A e. C /\ B e. C) -> {A, B} C_ C)

Syntax hints:   -> wi 4   /\ wa 358   e. wcel 1710   C_ wss 3258  {cpr 3739

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-un 3215  df-ss 3260  df-sn 3742  df-pr 3743

This theorem is referenced by: (None)