Theorem sbf2 1778

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 1541	. 2 |- F/ x A. x ph
2	1	sbf 1777	1 |- ( [ y / x ] A. x ph <-> A. x ph )

Syntax hints:   <-> wb 105   A.wal 1351   [wsb 1762

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-i9 1530  ax-ial 1534

This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763

This theorem is referenced by: (None)