3impib - New Foundations Explorer

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Theorem 3impib 1149

Description: Importation to triple conjunction. (Contributed by NM, 13-Jun-2006.)

**Hypothesis**
Ref	Expression
3impib.1	⊢ (φ → ((ψ ∧ χ) → θ))

**Assertion**
Ref	Expression
3impib	⊢ ((φ ∧ ψ ∧ χ) → θ)

**Proof of Theorem 3impib**
Step	Hyp	Ref	Expression
1		3impib.1	. . 3 ⊢ (φ → ((ψ ∧ χ) → θ))
2	1	exp3a 425	. 2 ⊢ (φ → (ψ → (χ → θ)))
3	2	3imp 1145	1 ⊢ ((φ ∧ ψ ∧ χ) → θ)

Colors of variables: wff setvar class

Syntax hints: → wi 4 ∧ wa 358 ∧ w3a 934

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8

This theorem depends on definitions: df-bi 177 df-an 360 df-3an 936

This theorem is referenced by: mob 3018 eqreu 3028 dedth3h 3705 peano5 4409 ncfinraise 4481 ncfinlower 4483 nnpweq 4523 spfininduct 4540 clos1induct 5880 3ecoptocl 5998 sbthlem2 6204