Theorem sbf2 1766

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 1529	. 2 |- F/ x A. x ph
2	1	sbf 1765	1 |- ( [ y / x ] A. x ph <-> A. x ph )

Syntax hints:   <-> wb 104   A.wal 1341   [wsb 1750

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1435  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-4 1498  ax-i9 1518  ax-ial 1522

This theorem depends on definitions:  df-bi 116  df-nf 1449  df-sb 1751

This theorem is referenced by: (None)