Theorem hbsb3 1205

Description: If y is not free in ph, x is not free in [y / x]ph.

Hypothesis

Ref	Expression
hbsb3.1	|- (ph -> A.yph)

Assertion

Ref	Expression
hbsb3	|- ([y / x]ph -> A.x[y / x]ph)

Proof of Theorem hbsb3

Step	Hyp	Ref	Expression
1		hbsb3.1	. . 3 |- (ph -> A.yph)
2	1	sbimi 1172	. 2 |- ([y / x]ph -> [y / x]A.yph)
3		hbsb2a 1203	. 2 |- ([y / x]A.yph -> A.x[y / x]ph)
4	2, 3	syl 10	1 |- ([y / x]ph -> A.x[y / x]ph)

Syntax hints:   -> wi 3  A.wal 953  [wsbc 1169

This theorem is referenced by:  ax16 1208  sbco2 1254  sb8 1260  ax16ALT 1270  mo 1392  axrepndlem1 4927  axrepndlem2 4928

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 962  ax-11 966  ax-4 972  ax-5o 974  ax-6o 977  ax-9o 1122

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 980  df-sb 1171

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