Theorem tposfn

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

	Ref	Expression
Assertion	tposfn	$$⊢FFn\left(A\times B\right)\to tposFFn\left(B\times A\right)$$

Proof

Step	Hyp	Ref	Expression
1		tposf	$$⊢F:A\times B⟶\mathrm{V}\to tposF:B\times A⟶\mathrm{V}$$
2		dffn2	$$⊢FFn\left(A\times B\right)\leftrightarrow F:A\times B⟶\mathrm{V}$$
3		dffn2	$$⊢tposFFn\left(B\times A\right)\leftrightarrow tposF:B\times A⟶\mathrm{V}$$
4	1 2 3	3imtr4i	$$⊢FFn\left(A\times B\right)\to tposFFn\left(B\times A\right)$$