Theorem import-P3.34a.RC 306

Description: Inference Form of import-P3.34a 305. †

Hypothesis

Ref	Expression
import-P3.34a.RC.1	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
import-P3.34a.RC	⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Proof of Theorem import-P3.34a.RC

Step	Hyp	Ref	Expression
1		import-P3.34a.RC.1	. . . 4 ⊢ (𝜑 → (𝜓 → 𝜒))
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → (𝜑 → (𝜓 → 𝜒)))
3	2	import-P3.34a 305	. 2 ⊢ (⊤ → ((𝜑 ∧ 𝜓) → 𝜒))
4	3	ndtruee-P3.18 183	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Syntax hints:   → wff-imp 10   ∧ wff-and 132  ⊤wff-true 153

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  df-true-D2.4 155

This theorem is referenced by:  example-E3.1b  310  dalloverimex-P5  605  lemma-L6.07a-L1  770  lemma-L6.07a-L2  771  splitelof-P6-L1  777  psubsuccv-P6-L1  805  lemma-L7.02a-L1  943  axL4-P7  945  nfrgencl-P7  965  allic-P7  1007  dalloverim-P7  1022  dalloverimex-P7  1033  qimeqex-P7-L1  1054