Theorem pm3.45 634

Description: Theorem *3.45 (Fact) of [WhiteheadRussell] p. 113. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm3.45	⊢ ((𝜑 → 𝜓) → ((𝜑 ∧ 𝜒) → (𝜓 ∧ 𝜒)))

Proof of Theorem pm3.45

Step	Hyp	Ref	Expression
1		id 23	. 2 ⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜓))
2	1	anim1d 623	1 ⊢ ((𝜑 → 𝜓) → ((𝜑 ∧ 𝜒) → (𝜓 ∧ 𝜒)))

This proof depends on syntax axioms:   → wi 4   ∧ wa 401

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402

This theorem is used by:  mopick  2651  ssrmof  3999  ssrexv  4001  rabss2OLD  4026  lmcnp  23602  fbflim2  24276  ivthlem2  25753  ivthlem3  25754  arg-ax  37174  pm10.56  45313