Theorem a4sbim 1244

Description: Specialization of implication.

Assertion

Ref	Expression
a4sbim	|- (A.x(ph -> ps) -> ([y / x]ph -> [y / x]ps))

Proof of Theorem a4sbim

Step	Hyp	Ref	Expression
1		stdpc4 1185	. 2 |- (A.x(ph -> ps) -> [y / x](ph -> ps))
2		sbim 1234	. 2 |- ([y / x](ph -> ps) <-> ([y / x]ph -> [y / x]ps))
3	1, 2	sylib 198	1 |- (A.x(ph -> ps) -> ([y / x]ph -> [y / x]ps))

Syntax hints:   -> wi 3  A.wal 953  [wsbc 1170

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 961  ax-gen 962  ax-10 965  ax-12 967  ax-4 972  ax-5o 974  ax-6o 977  ax-9o 1122  ax-10o 1139  ax-11o 1218

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 980  df-sb 1172

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