Theorem hbsb2a 1206

Description: Special case of a bound-variable hypothesis builder for substitution.

Assertion

Ref	Expression
hbsb2a	|- ([y / x]A.yph -> A.x[y / x]ph)

Proof of Theorem hbsb2a

Step	Hyp	Ref	Expression
1		sb4a 1201	. 2 |- ([y / x]A.yph -> A.x(x = y -> ph))
2		sb2 1179	. . 3 |- (A.x(x = y -> ph) -> [y / x]ph)
3	2	a5i 991	. 2 |- (A.x(x = y -> ph) -> A.x[y / x]ph)
4	1, 3	syl 10	1 |- ([y / x]A.yph -> A.x[y / x]ph)

Syntax hints:   -> wi 3  A.wal 956   = wceq 958  [wsbc 1172

This theorem is referenced by:  hbsb3 1208

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 965  ax-11 969  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125

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

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