Theorem rcp-NDORE2 235

Description: ∨ Elimination Recipe. †

Hypotheses

Ref	Expression
rcp-NDORE2.1	⊢ ((𝛾₁ ∧ 𝜑) → 𝜒)
rcp-NDORE2.2	⊢ ((𝛾₁ ∧ 𝜓) → 𝜒)
rcp-NDORE2.3	⊢ (𝛾₁ → (𝜑 ∨ 𝜓))

Assertion

Ref	Expression
rcp-NDORE2	⊢ (𝛾₁ → 𝜒)

Proof of Theorem rcp-NDORE2

Step	Hyp	Ref	Expression
1		rcp-NDORE2.1	. 2 ⊢ ((𝛾₁ ∧ 𝜑) → 𝜒)
2		rcp-NDORE2.2	. 2 ⊢ ((𝛾₁ ∧ 𝜓) → 𝜒)
3		rcp-NDORE2.3	. 2 ⊢ (𝛾₁ → (𝜑 ∨ 𝜓))
4	1, 2, 3	ndore-P3.12 177	1 ⊢ (𝛾₁ → 𝜒)

Syntax hints:   → wff-imp 10   ∧ wff-and 132   ∨ wff-or 144

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-or-D2.3 145

This theorem is referenced by:  orcomm-P3.37-L1  318  orassoc-P3.38-L1  320  orassoc-P3.38-L2  321  orasim-P3.48-L2  360  profeliml-P4.5a  385  profelimr-P4.5b  387  sepimorr-P4.9c  412  sepimandl-P4.9d  415  idorfalsel-P4.20a  440  idempotor-P4.25b  451  dmorgbrev-L4.4  455  andoveror-P4.27-L2  460  oroverand-P4.27-L3  462  oroverim-P4.28-L2  466  imasor-P4.32-L1  485  imasor-P4.32-L2  486  biasandorint-P4.34b  492  peirce-P4.40  511  exclmid2peirce-P4.41a  512  qimeqex-P7-L1  1054