Theorem sb5 1332

Description: Equivalence for substitution. Similar to Theorem 6.1 of [Quine] p. 40.

Assertion

Ref	Expression
sb5	|- ([y / x]ph <-> E.x(x = y /\ ph))

Distinct variable group:   x,y

Proof of Theorem sb5

Step	Hyp	Ref	Expression
1		sb6 1331	. 2 |- ([y / x]ph <-> A.x(x = y -> ph))
2		sb56 1330	. 2 |- (E.x(x = y /\ ph) <-> A.x(x = y -> ph))
3	1, 2	bitr4i 182	1 |- ([y / x]ph <-> E.x(x = y /\ ph))

Syntax hints:   -> wi 3   <-> wb 152   /\ wa 229  A.wal 1016   = wceq 1018  E.wex 1042  [wsbc 1233

This theorem is referenced by:  2sb5 1401  dfsb7 1406  sbelx 1410  subdefbi1 12318

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1025  ax-4 1035  ax-5o 1037  ax-6o 1040  ax-9o 1185  ax-16 1273  ax-11o 1281

This theorem depends on definitions:  df-bi 153  df-an 231  df-ex 1043  df-sb 1235

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