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Metamath Proof Explorer

Theorem simpli

Description: Inference eliminating a conjunct. (Contributed by NM, 15-Jun-1994)

Ref Expression
Hypothesis simpli.1 ⊢ ( 𝜑 ∧ 𝜓 )
Assertion simpli 𝜑

Proof

Step Hyp Ref Expression
1 simpli.1 ⊢ ( 𝜑 ∧ 𝜓 )
2 simpl ⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜑 )
3 1 2 ax-mp ⊢ 𝜑