Theorem adantlrl 474

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004.) (Proof shortened by Wolf Lammen, 4-Dec-2012.)

Hypothesis

Ref	Expression
adantl2.1	⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃)

Assertion

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

Proof of Theorem adantlrl

Step	Hyp	Ref	Expression
1		simpr 109	. 2 ⊢ ((𝜏 ∧ 𝜓) → 𝜓)
2		adantl2.1	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃)
3	1, 2	sylanl2 401	1 ⊢ (((𝜑 ∧ (𝜏 ∧ 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:  mapxpen  6814  recexgt0sr  7714  fsumabs  11406  fsumiun  11418