Theorem sb4b 1222

Description: Simplified definition of substitution when variables are distinct.

Assertion

Ref	Expression
sb4b	|- (-. A.x x = y -> ([y / x]ph <-> A.x(x = y -> ph)))

Proof of Theorem sb4b

Step	Hyp	Ref	Expression
1		sb4 1221	. 2 |- (-. A.x x = y -> ([y / x]ph -> A.x(x = y -> ph)))
2		sb2 1175	. 2 |- (A.x(x = y -> ph) -> [y / x]ph)
3	1, 2	impbid1 516	1 |- (-. A.x x = y -> ([y / x]ph <-> A.x(x = y -> ph)))

Syntax hints:  -. wn 2   -> wi 3   <-> wb 146  A.wal 952   = wceq 954  [wsbc 1168

This theorem is referenced by:  sbcom 1256  sbcom2 1332

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 960  ax-gen 961  ax-10 964  ax-12 966  ax-4 971  ax-5o 973  ax-6o 976  ax-9o 1121  ax-10o 1138  ax-11o 1216

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 979  df-sb 1170

Copyright terms: Public domain