Theorem ndnfrim-P7.3.RC 876

Description: Inference Form of ndnfrim-P7.3 828. †

Hypotheses

Ref	Expression
ndnfrim-P7.3.RC.1	⊢ Ⅎ𝑥𝜑
ndnfrim-P7.3.RC.2	⊢ Ⅎ𝑥𝜓

Assertion

Ref	Expression
ndnfrim-P7.3.RC	⊢ Ⅎ𝑥(𝜑 → 𝜓)

Proof of Theorem ndnfrim-P7.3.RC

Step	Hyp	Ref	Expression
1		ndnfrim-P7.3.RC.1	. . . 4 ⊢ Ⅎ𝑥𝜑
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → Ⅎ𝑥𝜑)
3		ndnfrim-P7.3.RC.2	. . . 4 ⊢ Ⅎ𝑥𝜓
4	3	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → Ⅎ𝑥𝜓)
5	2, 4	ndnfrim-P7.3 828	. 2 ⊢ (⊤ → Ⅎ𝑥(𝜑 → 𝜓))
6	5	ndtruee-P3.18 183	1 ⊢ Ⅎ𝑥(𝜑 → 𝜓)

Syntax hints:   → wff-imp 10  ⊤wff-true 153  Ⅎwff-nfree 681

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14  ax-GEN 15  ax-L4 16

This theorem depends on definitions:  df-bi-D2.1 107  df-and-D2.2 133  df-or-D2.3 145  df-true-D2.4 155  df-rcp-AND3 161  df-exists-D5.1 596  df-nfree-D6.1 682

This theorem is referenced by:  lemma-L7.02a-L1  943  dfnfreealtif-P7  964  qimeqallhalf-P7  975  qimeqex-P7-L1  1054