Theorem ad5ant12 509

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

Hypothesis

Ref	Expression
ad5ant2.1	⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Assertion

Ref	Expression
ad5ant12	⊢ (((((𝜑 ∧ 𝜓) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) → 𝜒)

Proof of Theorem ad5ant12

Step	Hyp	Ref	Expression
1		ad5ant2.1	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)
2	1	ad3antrrr 483	1 ⊢ (((((𝜑 ∧ 𝜓) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) → 𝜒)

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: (None)