Theorem hbsb3 1202

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 1169	. 2 |- ([y / x]ph -> [y / x]A.yph)
3		hbsb2a 1200	. 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 951  [wsbc 1166

This theorem is referenced by:  ax16 1205  sbco2 1250  sb8 1256  ax16ALT 1266  mo 1386  axrepndlem1 4916  axrepndlem2 4917

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 960  ax-11 964  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 978  df-sb 1168

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