Theorem sbf2 1719

Description: Substitution has no effect on a bound variable. (Contributed by NM, 1-Jul-2005.)

Assertion

Ref	Expression
sbf2	|- ( [ y / x ] A. x ph <-> A. x ph )

Proof of Theorem sbf2

Step	Hyp	Ref	Expression
1		nfa1 1489	. 2 |- F/ x A. x ph
2	1	sbf 1718	1 |- ( [ y / x ] A. x ph <-> A. x ph )

Syntax hints:   <-> wb 104   A.wal 1297   [wsb 1703

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1391  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-4 1455  ax-i9 1478  ax-ial 1482

This theorem depends on definitions:  df-bi 116  df-nf 1405  df-sb 1704

This theorem is referenced by: (None)