Theorem ad4ant24 1290

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

Hypothesis

Ref	Expression
ad4ant24.1	⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Assertion

Ref	Expression
ad4ant24	⊢ ((((𝜃 ∧ 𝜑) ∧ 𝜏) ∧ 𝜓) → 𝜒)

Proof of Theorem ad4ant24

Step	Hyp	Ref	Expression
1		ad4ant24.1	. . . 4 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)
2	1	ex 449	. . 3 ⊢ (𝜑 → (𝜓 → 𝜒))
3	2	a1i13 27	. 2 ⊢ (𝜃 → (𝜑 → (𝜏 → (𝜓 → 𝜒))))
4	3	imp41 617	1 ⊢ ((((𝜃 ∧ 𝜑) ∧ 𝜏) ∧ 𝜓) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 383

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 196  df-an 385

This theorem is referenced by:  matunitlindflem1  32575  matunitlindflem2  32576  founiiun0  38372  xralrple2  38511  sge0iunmptlemre  39308  nnfoctbdjlem  39348  iundjiun  39353  hoidmvlelem3  39487  hspmbllem2  39517  smflimlem2  39658  av-numclwlk1lem2f1  41524