Theorem sbalv 1351

Description: Quantify with new variable inside substitution.

Hypothesis

Ref	Expression
sbalv.1	|- ([y / x]ph <-> ps)

Assertion

Ref	Expression
sbalv	|- ([y / x]A.zph <-> A.zps)

Distinct variable groups:   x,z   y,z

Proof of Theorem sbalv

Step	Hyp	Ref	Expression
1		sbal 1349	. 2 |- ([y / x]A.zph <-> A.z[y / x]ph)
2		sbalv.1	. . 3 |- ([y / x]ph <-> ps)
3	2	albii 1001	. 2 |- (A.z[y / x]ph <-> A.zps)
4	1, 3	bitr 173	1 |- ([y / x]A.zph <-> A.zps)

Syntax hints:   <-> wb 146  A.wal 956  [wsbc 1172

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-9 967  ax-10 968  ax-12 970  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 983  df-sb 1174

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