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Theorem f1oeq2d 38356
 Description: Equality deduction for one-to-one onto functions. (Contributed by Glauco Siliprandi, 17-Aug-2020.)
Hypothesis
Ref Expression
f1oeq2d.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
f1oeq2d (𝜑 → (𝐹:𝐴1-1-onto𝐶𝐹:𝐵1-1-onto𝐶))

Proof of Theorem f1oeq2d
StepHypRef Expression
1 f1oeq2d.1 . 2 (𝜑𝐴 = 𝐵)
2 f1oeq2 6041 . 2 (𝐴 = 𝐵 → (𝐹:𝐴1-1-onto𝐶𝐹:𝐵1-1-onto𝐶))
31, 2syl 17 1 (𝜑 → (𝐹:𝐴1-1-onto𝐶𝐹:𝐵1-1-onto𝐶))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 195   = wceq 1475  –1-1-onto→wf1o 5803 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-an 385  df-cleq 2603  df-fn 5807  df-f 5808  df-f1 5809  df-fo 5810  df-f1o 5811 This theorem is referenced by: (None)
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