Theorem 3adant2r 1235

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)

Hypothesis

Ref	Expression
3adant1l.1	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)

Assertion

Ref	Expression
3adant2r	⊢ ((𝜑 ∧ (𝜓 ∧ 𝜏) ∧ 𝜒) → 𝜃)

Proof of Theorem 3adant2r

Step	Hyp	Ref	Expression
1		3adant1l.1	. . . 4 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)
2	1	3com12 1209	. . 3 ⊢ ((𝜓 ∧ 𝜑 ∧ 𝜒) → 𝜃)
3	2	3adant1r 1233	. 2 ⊢ (((𝜓 ∧ 𝜏) ∧ 𝜑 ∧ 𝜒) → 𝜃)
4	3	3com12 1209	1 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜏) ∧ 𝜒) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 980

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 982

This theorem is referenced by:  caovimo  6117  mulassnqg  7451  prarloc  7570  ltexprlemfl  7676  ltexprlemfu  7678  addasssrg  7823  axaddass  7939