Theorem ad4ant134 1296

Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.)

Hypothesis

Ref	Expression
ad4ant134.1	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)

Assertion

Ref	Expression
ad4ant134	⊢ ((((𝜑 ∧ 𝜏) ∧ 𝜓) ∧ 𝜒) → 𝜃)

Proof of Theorem ad4ant134

Step	Hyp	Ref	Expression
1		ad4ant134.1	. . . 4 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)
2	1	3exp 1264	. . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃)))
3	2	a1d 25	. 2 ⊢ (𝜑 → (𝜏 → (𝜓 → (𝜒 → 𝜃))))
4	3	imp41 619	1 ⊢ ((((𝜑 ∧ 𝜏) ∧ 𝜓) ∧ 𝜒) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 384   ∧ w3a 1037

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386  df-3an 1039

This theorem is referenced by:  ralxfrd2  4884  wlkpwwlkf1ouspgr  26765  numclwlk1lem2foa  27224  climxlim2lem  40071  smflimlem4  40982