Theorem pm10.14 38558

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

Step	Hyp	Ref	Expression
1		stdpc4 2353	. 2 ⊢ (∀𝑥𝜑 → [𝑦 / 𝑥]𝜑)
2		stdpc4 2353	. 2 ⊢ (∀𝑥𝜓 → [𝑦 / 𝑥]𝜓)
3	1, 2	anim12i 590	1 ⊢ ((∀𝑥𝜑 ∧ ∀𝑥𝜓) → ([𝑦 / 𝑥]𝜑 ∧ [𝑦 / 𝑥]𝜓))

Syntax hints:   → wi 4   ∧ wa 384  ∀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)