Theorem pm2.04 31

Description: Swap antecedents. Theorem *2.04 of [WhiteheadRussell] p. 100.

Assertion

Ref	Expression
pm2.04	⊢ ((φ → (ψ → χ)) → (ψ → (φ → χ)))

Proof of Theorem pm2.04

Step	Hyp	Ref	Expression
1		ax-2 4	. 2 ⊢ ((φ → (ψ → χ)) → ((φ → ψ) → (φ → χ)))
2		ax-1 3	. 2 ⊢ (ψ → (φ → ψ))
3	1, 2	syl5 22	1 ⊢ ((φ → (ψ → χ)) → (ψ → (φ → χ)))

Syntax hints:   → wi 2

This theorem is referenced by:  com23 32  com34 36  bi2.04 141  ralcom3 1315  suppsr3 4018

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-mp 6

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