Theorem adantlrr 487

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
adantlrr	⊢ (((𝜑 ∧ (𝜓 ∧ 𝜏)) ∧ 𝜒) → 𝜃)

Proof of Theorem adantlrr

Step	Hyp	Ref	Expression
1		simpl 109	. 2 ⊢ ((𝜓 ∧ 𝜏) → 𝜓)
2		adantl2.1	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃)
3	1, 2	sylanl2 407	1 ⊢ (((𝜑 ∧ (𝜓 ∧ 𝜏)) ∧ 𝜒) → 𝜃)

This proof depends on syntax axioms:   → wi 4   ∧ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is used by:  exmidfodomrlemim  7560  distrlem1prl  7956  distrlem1pru  7957  cnegex  8512  lcmgcdlem  12881  lcmdvds  12883  ballotfilemfc0  13291  ballotfilemfcc  13292  conjnmzb  14143  metss2lem  15735  dvmptfsum  15963