Theorem stdpc4 2094

Description: The specialization axiom of standard predicate calculus. It states that if a statement holds for all , then it also holds for the specific case of (properly) substituted for . Translated to traditional notation, it can be read: "A.x(x)->(), provided that is free for in (x)." Axiom 4 of [Mendelson] p. 69. See also spsbc 3340 and rspsbc 3417. (Contributed by NM, 14-May-1993.)

Assertion

Ref	Expression
stdpc4

Proof of Theorem stdpc4

Step	Hyp	Ref	Expression
1		ala1 1660	. 2
2		sb2 2093	. 2
3	1, 2	syl 16	1

Syntax hints:  ->wi 4  A.wal 1393  [wsb 1739

This theorem is referenced by:  2stdpc4  2095  sbft  2120  spsbim  2135  spsbbi  2143  sbt  2162  sbtrt  2163  pm13.183  3240  spsbc  3340  nd1  8983  nd2  8984  pm10.14  31264  pm11.57  31295  bj-vexwt  34430  axfrege58b  37927

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-12 1854  ax-13 1999

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-sb 1740