Theorem ssmin 2552

Description: Subclass of the minimum value of class of supersets.

Assertion

Ref	Expression
ssmin	|- A (_ |^|{x | (A (_ x /\ ph)}

Distinct variable group:   x,A

Proof of Theorem ssmin

Step	Hyp	Ref	Expression
1		ssintab 2550	. 2 |- (A (_ |^|{x | (A (_ x /\ ph)} <-> A.x((A (_ x /\ ph) -> A (_ x))
2		pm3.26 319	. 2 |- ((A (_ x /\ ph) -> A (_ x)
3	1, 2	mpgbir 988	1 |- A (_ |^|{x | (A (_ x /\ ph)}

Syntax hints:   -> wi 3   /\ wa 223  {cab 1463   (_ wss 2047  |^|cint 2533

This theorem is referenced by:  abfii4OLD 4564

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-ral 1649  df-v 1812  df-in 2051  df-ss 2053  df-int 2534

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