ndander-P3.9 - bfol.mm Proof Explorer

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Theorem ndander-P3.9 174

Description: Natural Deduction: Right '∧' Elimination Rule.

Deduce the left conjunct (i.e. eliminate the right conjunct) of a previously deduced conjunction.

**Hypothesis**
Ref	Expression
ndander-P3.9.1	⊢ (𝛾 → (𝜑 ∧ 𝜓))

**Assertion**
Ref	Expression
ndander-P3.9	⊢ (𝛾 → 𝜑)

**Proof of Theorem ndander-P3.9**
Step	Hyp	Ref	Expression
1		ndander-P3.9.1	. 2 ⊢ (𝛾 → (𝜑 ∧ 𝜓))
2	1	simpl-P2.9a.AC.SH 135	1 ⊢ (𝛾 → 𝜑)

Colors of variables: wff objvar term class

Syntax hints: → wff-imp 10 ∧ wff-and 132

This theorem was proved from axioms: ax-L1 11 ax-L2 12 ax-L3 13 ax-MP 14

This theorem depends on definitions: df-bi-D2.1 107 df-and-D2.2 133