Theorem ssmin 2548

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 2546	. 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 987	1 |- A (_ |^|{x | (A (_ x /\ ph)}

Syntax hints:   -> wi 3   /\ wa 223  {cab 1462   (_ wss 2044  |^|cint 2529

This theorem is referenced by:  abfii4 4547

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 961  ax-gen 962  ax-8 963  ax-10 965  ax-12 967  ax-17 970  ax-4 972  ax-5o 974  ax-6o 977  ax-9o 1122  ax-10o 1139  ax-16 1209  ax-11o 1217  ax-ext 1458

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 980  df-sb 1171  df-clab 1463  df-cleq 1468  df-clel 1471  df-ral 1647  df-v 1809  df-in 2048  df-ss 2050  df-int 2530

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