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Metamath Proof Explorer

Theorem tposfn

Description: Functionality of a transposition. (Contributed by Mario Carneiro, 4-Oct-2015)

		Ref	Expression
	Assertion	tposfn	$⊢ F Fn (A \times B) \to tpos F Fn (B \times A)$

Step	Hyp	Ref	Expression
1		tposf	$⊢ F : A \times B ⟶ V \to tpos F : B \times A ⟶ V$
2		dffn2	$⊢ F Fn (A \times B) \leftrightarrow F : A \times B ⟶ V$
3		dffn2	$⊢ tpos F Fn (B \times A) \leftrightarrow tpos F : B \times A ⟶ V$
4	1 2 3	3imtr4i	$⊢ F Fn (A \times B) \to tpos F Fn (B \times A)$