Theorem impl 378

Description: Export a wff from a left conjunct. (Contributed by Mario Carneiro, 9-Jul-2014.)

Hypothesis

Ref	Expression
impl.1	⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃))

Assertion

Ref	Expression
impl	⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃)

Proof of Theorem impl

Step	Hyp	Ref	Expression
1		impl.1	. . 3 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → 𝜃))
2	1	expd 256	. 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
3	2	imp31 254	1 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem is referenced by:  sbc2iedv  3027  csbie2t  3097  foco2  5733  erth  6557  distrlem1prl  7544  distrlem1pru  7545  uz11  9509  elpq  9607  divgcdcoprm0  12055  cncongr1  12057  prmpwdvds  12307  efltlemlt  13489