Theorem pm11.11 45125

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 2107	. . 3 ⊢ (∀𝑥∀𝑦𝜑 → [𝑧 / 𝑥][𝑤 / 𝑦]𝜑)
2		pm11.11.1	. . . 4 ⊢ 𝜑
3	2	ax-gen 1828	. . 3 ⊢ ∀𝑦𝜑
4	1, 3	mpg 1830	. 2 ⊢ [𝑧 / 𝑥][𝑤 / 𝑦]𝜑
5	4	gen2 1829	1 ⊢ ∀𝑧∀𝑤[𝑧 / 𝑥][𝑤 / 𝑦]𝜑

This proof depends on syntax axioms:  ∀wal 1568  [wsb 2099

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1813  df-sb 2100

This theorem is used by: (None)