Theorem feq3d 5353

Description: Equality deduction for functions. (Contributed by AV, 1-Jan-2020.)

Hypothesis

Ref	Expression
feq2d.1	|- ( ph -> A = B )

Assertion

Ref	Expression
feq3d	|- ( ph -> ( F : X --> A <-> F : X --> B ) )

Proof of Theorem feq3d

Step	Hyp	Ref	Expression
1		feq2d.1	. 2 |- ( ph -> A = B )
2		feq3 5349	. 2 |- ( A = B -> ( F : X --> A <-> F : X --> B ) )
3	1, 2	syl 14	1 |- ( ph -> ( F : X --> A <-> F : X --> B ) )

Syntax hints:   -> wi 4   <-> wb 105   = wceq 1353   -->wf 5211

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-in 3135  df-ss 3142  df-f 5219

This theorem is referenced by:  uptx  13645  txcn  13646