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Theorem pm10.14 37383
Description: Theorem *10.14 in [WhiteheadRussell] p. 146. (Contributed by Andrew Salmon, 17-Jun-2011.)
Assertion
Ref Expression
pm10.14 ((∀𝑥𝜑 ∧ ∀𝑥𝜓) → ([𝑦 / 𝑥]𝜑 ∧ [𝑦 / 𝑥]𝜓))

Proof of Theorem pm10.14
StepHypRef Expression
1 stdpc4 2340 . 2 (∀𝑥𝜑 → [𝑦 / 𝑥]𝜑)
2 stdpc4 2340 . 2 (∀𝑥𝜓 → [𝑦 / 𝑥]𝜓)
31, 2anim12i 587 1 ((∀𝑥𝜑 ∧ ∀𝑥𝜓) → ([𝑦 / 𝑥]𝜑 ∧ [𝑦 / 𝑥]𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  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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