Theorem simpr-P2.9b 136

Description: '∧' Right Simplification.

Assertion

Ref	Expression
simpr-P2.9b	⊢ ((𝜑 ∧ 𝜓) → 𝜓)

Proof of Theorem simpr-P2.9b

Step	Hyp	Ref	Expression
1		df-and-D2.2 133	. . 3 ⊢ ((𝜑 ∧ 𝜓) ↔ ¬ (𝜑 → ¬ 𝜓))
2	1	bifwd-P2.5a.SH 112	. 2 ⊢ ((𝜑 ∧ 𝜓) → ¬ (𝜑 → ¬ 𝜓))
3		simpr-L2.2b 97	. 2 ⊢ (¬ (𝜑 → ¬ 𝜓) → 𝜓)
4	2, 3	syl-P1.2 34	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)

Syntax hints:  ¬ wff-neg 9   → 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

This theorem is referenced by:  simpr-P2.9b.AC.SH  137  import-P2.10a  140  orelim-P2.11c  150  ndasm-P3.1  166