Theorem stdpc4-2 16322

Description: Theorem *11.1 in [WhiteheadRussell] p. 159.

Assertion

Ref	Expression
stdpc4-2	|- (A.xA.yph -> [z / x][w / y]ph)

Proof of Theorem stdpc4-2

Step	Hyp	Ref	Expression
1		stdpc4 1550	. . 3 |- (A.yph -> [w / y]ph)
2	1	alimi 1338	. 2 |- (A.xA.yph -> A.x[w / y]ph)
3		stdpc4 1550	. 2 |- (A.x[w / y]ph -> [z / x][w / y]ph)
4	2, 3	syl 12	1 |- (A.xA.yph -> [z / x][w / y]ph)

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

This theorem is referenced by:  pm11.11 16323

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1305  ax-4 1319  ax-5o 1321  ax-6o 1324  ax-9o 1481

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

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