Theorem feq3d 5326

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 5322	. 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 104   = wceq 1343   -->wf 5184

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-11 1494  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-nf 1449  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-in 3122  df-ss 3129  df-f 5192

This theorem is referenced by:  uptx  12914  txcn  12915