Theorem a4sbim 1614

Description: Specialization of implication. (The proof was shortened by Andrew Salmon, 25-May-2011.)

Assertion

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

Proof of Theorem a4sbim

Step	Hyp	Ref	Expression
1		stdpc4 1550	. 2 |- (A.x(ph -> ps) -> [y / x](ph -> ps))
2		sbi1 1602	. 2 |- ([y / x](ph -> ps) -> ([y / x]ph -> [y / x]ps))
3	1, 2	syl 12	1 |- (A.x(ph -> ps) -> ([y / x]ph -> [y / x]ps))

Syntax hints:   -> wi 3  A.wal 1296  [wsbc 1534

This theorem is referenced by:  sbf3t 1619  hbsb4t 1621  pm11.59 16348  sbiota1 16399

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 1304  ax-gen 1305  ax-10 1308  ax-12 1310  ax-4 1319  ax-5o 1321  ax-6o 1324  ax-9o 1481  ax-10o 1500  ax-11o 1588

This theorem depends on definitions:  df-bi 164  df-an 242  df-ex 1327  df-sb 1536

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