Theorem syldc 46

Description: Syllogism deduction. Commuted form of syld 45. (Contributed by BJ, 25-Oct-2021.)

Hypotheses

Ref	Expression
syld.1	⊢ (𝜑 → (𝜓 → 𝜒))
syld.2	⊢ (𝜑 → (𝜒 → 𝜃))

Assertion

Ref	Expression
syldc	⊢ (𝜓 → (𝜑 → 𝜃))

Proof of Theorem syldc

Step	Hyp	Ref	Expression
1		syld.1	. . 3 ⊢ (𝜑 → (𝜓 → 𝜒))
2		syld.2	. . 3 ⊢ (𝜑 → (𝜒 → 𝜃))
3	1, 2	syld 45	. 2 ⊢ (𝜑 → (𝜓 → 𝜃))
4	3	com12 30	1 ⊢ (𝜓 → (𝜑 → 𝜃))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  dfgrp3mlem  13300