Theorem imcomm-P1.6.SH 49

Description: Inference from imcomm-P1.6 48.

Hypothesis

Ref	Expression
imcomm-P1.6.SH.1	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
imcomm-P1.6.SH	⊢ (𝜓 → (𝜑 → 𝜒))

Proof of Theorem imcomm-P1.6.SH

Step	Hyp	Ref	Expression
1		imcomm-P1.6.SH.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
2		imcomm-P1.6 48	. 2 ⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜓 → (𝜑 → 𝜒)))
3	1, 2	ax-MP 14	1 ⊢ (𝜓 → (𝜑 → 𝜒))

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:  imsubl-P1.7b  54  mpt-P1.8  57  poe-P1.11b  66