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	⊢ 𝜑

Assertion

Ref	Expression
pm11.11	⊢ ∀𝑧∀𝑤[𝑧 / 𝑥][𝑤 / 𝑦]𝜑

Proof of Theorem pm11.11

Step	Hyp	Ref	Expression
1		2stdpc4 2354	. . 3 ⊢ (∀𝑥∀𝑦𝜑 → [𝑧 / 𝑥][𝑤 / 𝑦]𝜑)
2		pm11.11.1	. . . 4 ⊢ 𝜑
3	2	ax-gen 1722	. . 3 ⊢ ∀𝑦𝜑
4	1, 3	mpg 1724	. 2 ⊢ [𝑧 / 𝑥][𝑤 / 𝑦]𝜑
5	4	gen2 1723	1 ⊢ ∀𝑧∀𝑤[𝑧 / 𝑥][𝑤 / 𝑦]𝜑

Syntax hints:  ∀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)