Theorem rcp-NDIME0 228

Description: This is the same is ax-MP 14. †

Hypotheses

Ref	Expression
rcp-NDIME0.1	⊢ 𝜑
rcp-NDIME0.2	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
rcp-NDIME0	⊢ 𝜓

Proof of Theorem rcp-NDIME0

Step	Hyp	Ref	Expression
1		rcp-NDIME0.1	. . . 4 ⊢ 𝜑
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → 𝜑)
3		rcp-NDIME0.2	. . . 4 ⊢ (𝜑 → 𝜓)
4	3	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → (𝜑 → 𝜓))
5	2, 4	ndime-P3.6 171	. 2 ⊢ (⊤ → 𝜓)
6	5	ndtruee-P3.18 183	1 ⊢ 𝜓

Syntax hints:   → wff-imp 10  ⊤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-true-D2.4 155

This theorem is referenced by:  idandtruer-P4.19b  439  idorfalser-P4.20b  441  idandthml-P4.23a  446  idandthmr-P4.23b  447  idornthml-P4.24a  448  idornthmr-P4.24b  449  peirce2exclmid-P4.41b  513  exiav-P5.SH  616  spliteq-P6  776  splitelof-P6  778  nfrterm-P6  779  psubim-P6-L2  790  ndnfrneg-P7.2  827  alli-P7  947  axL6-P7  961  example-E7.1b  1075