Theorem 3ad2antr1 1069

Description: Deduction adding a conjuncts to antecedent. (Contributed by NM, 25-Dec-2007.)

Hypothesis

Ref	Expression
3ad2antl.1	⊢ ((𝜑 ∧ 𝜒) → 𝜃)

Assertion

Ref	Expression
3ad2antr1	⊢ ((𝜑 ∧ (𝜒 ∧ 𝜓 ∧ 𝜏)) → 𝜃)

Proof of Theorem 3ad2antr1

Step	Hyp	Ref	Expression
1		3ad2antl.1	. . 3 ⊢ ((𝜑 ∧ 𝜒) → 𝜃)
2	1	adantrr 448	. 2 ⊢ ((𝜑 ∧ (𝜒 ∧ 𝜓)) → 𝜃)
3	2	3adantr3 1065	1 ⊢ ((𝜑 ∧ (𝜒 ∧ 𝜓 ∧ 𝜏)) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 97   ∧ w3a 885

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-3an 887

This theorem is referenced by:  ispod  4041  poxp  5853  fzosubel2  9051