Theorem id-P1.4 36

Description: Implication Identity.

Assertion

Ref	Expression
id-P1.4	⊢ (𝜑 → 𝜑)

Proof of Theorem id-P1.4

Step	Hyp	Ref	Expression
1		ax-L1 11	. 2 ⊢ (𝜑 → (𝜑 → 𝜑))
2		ax-L1 11	. . 3 ⊢ (𝜑 → ((𝜑 → 𝜑) → 𝜑))
3	2	axL2.SH 31	. 2 ⊢ ((𝜑 → (𝜑 → 𝜑)) → (𝜑 → 𝜑))
4	1, 3	ax-MP 14	1 ⊢ (𝜑 → 𝜑)

Syntax hints:   → wff-imp 10

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-MP 14

This theorem is referenced by:  rae-P1.5  37  mpt-P1.8  57  simpr-L2.2b  97  cmb-L2.3  99  bijust-P2.2-L1  105  biref-P2.6a  123  bitrns-P2.6c  126  truejust-P2.13  154  true-P2.14  156