Theorem pm11.11 38573

Description: Theorem *11.11 in [WhiteheadRussell] p. 159. (Contributed by Andrew Salmon, 17-Jun-2011.)

Hypothesis

Ref	Expression
pm11.11.1	|- ph

Assertion

Ref	Expression
pm11.11	|- A. z A. w [ z / x ] [ w / y ] ph

Proof of Theorem pm11.11

Step	Hyp	Ref	Expression
1		2stdpc4 2354	. . 3 |- ( A. x A. y ph -> [ z / x ] [ w / y ] ph )
2		pm11.11.1	. . . 4 |- ph
3	2	ax-gen 1722	. . 3 |- A. y ph
4	1, 3	mpg 1724	. 2 |- [ z / x ] [ w / y ] ph
5	4	gen2 1723	1 |- A. z A. w [ z / x ] [ w / y ] ph

Syntax hints:   A.wal 1481   [wsb 1880

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-sb 1881

This theorem is referenced by: (None)