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Theorem pm11.11 37398
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 𝑧𝑤[𝑧 / 𝑥][𝑤 / 𝑦]𝜑

Proof of Theorem pm11.11
StepHypRef Expression
1 2stdpc4 2341 . . 3 (∀𝑥𝑦𝜑 → [𝑧 / 𝑥][𝑤 / 𝑦]𝜑)
2 pm11.11.1 . . . 4 𝜑
32ax-gen 1712 . . 3 𝑦𝜑
41, 3mpg 1714 . 2 [𝑧 / 𝑥][𝑤 / 𝑦]𝜑
54gen2 1713 1 𝑧𝑤[𝑧 / 𝑥][𝑤 / 𝑦]𝜑
Colors of variables: wff setvar class
Syntax hints:  wal 1472  [wsb 1866
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-12 2032  ax-13 2232
This theorem depends on definitions:  df-bi 195  df-an 384  df-ex 1695  df-sb 1867
This theorem is referenced by: (None)
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