Theorem mpan121 533

Description: An inference based on modus ponens.

Hypotheses

Ref	Expression
mpan121.1	⊢ ψ
mpan121.2	⊢ (((φ ∧ (ψ ∧ χ)) ∧ θ) → τ)

Assertion

Ref	Expression
mpan121	⊢ (((φ ∧ χ) ∧ θ) → τ)

Proof of Theorem mpan121

Step	Hyp	Ref	Expression
1		mpan121.1	. . 3 ⊢ ψ
2		mpan121.2	. . . 4 ⊢ (((φ ∧ (ψ ∧ χ)) ∧ θ) → τ)
3	2	exp 291	. . 3 ⊢ ((φ ∧ (ψ ∧ χ)) → (θ → τ))
4	1, 3	mpan21 531	. 2 ⊢ ((φ ∧ χ) → (θ → τ))
5	4	imp 277	1 ⊢ (((φ ∧ χ) ∧ θ) → τ)

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  oecl 3140  oen0 3165

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

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